In this thesis, at the first a one-step wet chemical method was used to synthesis of reduced graphene oxide nanoflakes (2D RGONF) from graphite by a thermal reduction at low temperature. This method is simple and avoids the usage of harmful chemical reductants. Then, a new electrocatalyst consist of Ni-Co-Se nanoparticles were deposited on RGONF ( Ni-Co-Se@RGONF ) by solvothermaly method. The average size of nanoparticles which deposited on RGONF was about 80 nm. Then, a glassy carbon electrode (GCE) was modified with Ni-Co-Se@RGONF and was used as an electrocatalyst for hydrogen evolution reaction (HER) in 0.50 mol L-1 sulfuric acid. The results show that the RGONF/Ni-Co-Se has an excellent catalytic activity toward HER with overpotential ,Tafel slope and stability about 5 mV (vs. RHE) , 30±3 mV decade-1 and at least 20days in sulfuric acid, respectively. These results are comparable with C/Pt(20%) as a commercial electrocatalyst for HER. At the second study, a new hybrid material consisting Co(OH)2 magnetic nanoflake (MNF-Co(OH)2) grown on reduced graphene oxide nanoflake (MNF-Co(OH)2@RGONF) was synthesized by a facile and inexpensive technique. Then the MNF-Co(OH)2@RGONF/GCE was used as a bi-functional electrocatalyst for the OER and ORR in alkaline media. The onset potential, current density at 2.025 V (vs. RHE), and Tafel slope of OER in 1.0 mol L-1 KOH for MNF-Co(OH)2@RGONF modified glassy carbon electrode (MNF-Co(OH)2@RGONF/GCE) were about 1.505 mV (vs. RHE), 227 mA cm-2 and 63 mV dec-1, respectively. So that the current density and Tafel slope of this electrocatalyst are better than commercial IrO2. Furthermore, it was concluded that MNF-Co(OH)2@RGONF/GCE due to four-electron transfer mechanism, better durability and stronger resistance rather than Pt/C (20%) at 0.436 V in KOH 0.10 mol L-1 (with the addition of methanol to electrochemical cell), has a high catalytic activity for ORR. At the 3th study, a new synthesis of Co(OH)2@RGONF nanohybrid via a facile hydrothermal procedure for feasible operation as a supercapacitor compound and OER electrocatalyst in alkaline media. The Co(OH)2@RGONF/GCE as a supercapacitor electrode with potential windows of 0.35 V, exhibits a powerful specific capacitance (235.20 F g?1 at 0.1 A g?1 current density), energy density, stability (about 90% of the initial capacitance value maintain after 2000 cycles at 1.0 A g?1) and fast charge/discharge ability. Furthermore, the modified electrode displays a good electrocatalytic activity for oxygen evolution reaction with a current density of 10.0 mA cm-2 at 1.647 V, small Tafel slope of 56.5 mV dec-1, good onset potential of 1.521 V vs. RHE and suitable durability. At the 4th study, the porous magnetic iron manganese oxide nanoparticles (PMFMO) with hollow structure (the pore sizes on the surface of cubes are about 10 nm) were created from metal organic frame work and deposited on the RGONF by a thermal method. After that, the modified GCE were investigated with PMFMO@RGONF nanocomposite as a low-cost electrocatalyst for HER (in acidic media) and ORR (in alkaline media). The Tafel slope of PMFMO@RGONF nanocomposite is about 107 mV dec-1 in the 0.5 mol L-1 H2SO4 solution and suggests the Volmer–Heyrovsky mechanism for HER. The results show that this electrocatalyst has an excellent stability (at least 10000 cycles) in the sulfuric acid solution. Hence, The LSV curve shows that the Pt(20%)/C has a better onset-potential than present electrocatalyst for HER but PMFMO@RGONF nanocomposite produces current density (j) of 300 mA cm-2 at overpotential (?) of -721 mV (?300 = -721 mV(vs. Ag/AgCl)) which is smaller than Pt(20%)/C (?300 = -802 mV). The PMFMO@RGONF nanocomposite as an electrocatalyst follows four electrons mechanism for ORR in 0.10 mol. L-1 KOH. As an important result, after addition of methanol into the electrolyte, this electrocatalyst is stable for a long time (at least 10000s) while the catalytic activity of Pt (20%)/C is quickly lost in the presence of methanol. At the final study, the 3D graphene (3D-G) is synthesized with a single flake of GO and Iron (???) chloride. This method is simple and inexpensive. The TEM result show that the Iron nanoparticles with an average size of 8 nm deposited on 3D-G. Then, the GCE which modified by 3D-G is used as an electrocatalyst for HER in acidic and alkaline media. The results show that excellent catalytic activities, Tafel slope, onset potential and stability for this nanocomposite. According to the results, this nanocomposite as an inexpensive electrocatalyst can be used as a substitute for carbon-platinum commercial electrocatalyst in HER.