In recent years, bypass ratio has been attended by gas turbine experts and companies as an affecting parameter on specific fuel consumption reduction, maximum total range enhancement and environmental pollution decrement in civil turbofan engines. On the other hand, total pressure ratio, efficiency and surge margin are significant parameters in aerodynamic design of compressor and fan. In present research first a novel one-dimensional design method based on the radial equilibrium theory and constant span-wise diffusion factor has been presented to redesign a compressor stage and a fan rotor. Because of very high pressure ratio and low efficiency in fan rotor with constant span-wise diffusion factor, the distribution of diffusion factor has been used to redesign the fan once again to achieve not only higher efficiency and pressure ratio simultaneously, but also to achieve better surge margin and more bypass air in constant diameter. A one-dimensional design code has been developed to obtain the meridional plane and blade to blade geometry of rotor such as blade thickness and angle distribution to reach the three-dimensional view of the rotor blades. To verify the redesigned rotor, its flow numerical simulation has been carried out to compute its performance curve. The experimental data, available for the performance curve and span-wise thermodynamic parameters of NASA Rotor67, has been used to validate the results of the numerical simulation and one-dimensional code. Structured mesh with finer grids near walls has been used to capture flow field and boundary layer effects. RANS equations using shear stress traort turbulence model were solved by finite volume method for rotating and stationary zones. The numerical results of the new compressor stage have showed about 18% improvement in its total pressure ratio and 11% increase in its efficiency at both design and off design mass flow rate. Unfortunately, mass flow rate of the redesigned compressor stage has decreased about 5.7% because of inappropriate incidence and deviation angle correlation. This problem has been solved in fan rotor design by finding incidence and deviation angle from the simulation results. The numerical results of the new fan rotor which was designed based on constant diffusion factor have showed about 9.6% increase in its total pressure ratio at both design and off design mass flow rate in comparison to rotor67. As a result of increasing fan pressure ratio, the efficiency has decreased about 3.5%. The second fan rotor which has been designed based on distribution of diffusion factor, has showed about 3% improvement in pressure ratio, 1.6% efficiency enhancement and 125% increase in surge margin by comparison with rotor67. The thermodynamic analysis of turbofan cycle has been done to evaluate fan operation in turbofan engine. Both of the new designed fan, especially constant diffusion one have had better performance in turbofan engine in comparison to NASA rotor67. The constant diffusion rotor has had the most outlet velocity especially in upper span which could improve bypass ratio by about 10% by transferring more mass flow to the cold bypass duct of a turbofan engine. Because of increasing bypass ratio, average specific fuel consumption has decreased about 6%. Keywords: Transonic axial fan and compressor, One-dimensional design, Numerical simulation, Radial equilibrium, Thermodynamic analysis of turbofan cycle.