Synchronization phenomena in population of interacting elements are the subject of intense research efforts in physics, chemistry, biology and social science. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this thesis after introducing the synchronization phenomena, the stability of frequency synchronization in complex networks is analyzed in kuramorto model. First, we investigate the synchronization of two oscillators and find out how the difference between natural frequencies will affect the stability state of synchronization and then find out in which condition they could get the fully synchronized state. Then we introduce the complex networks, and became familiar with Small-World, Scale-Free, Random and Regular networks and teach how we can model them in computer. More than that, we will familiar with "clustering coefficient" and "the shortest path length" which are two important aspects of networks. Then we model the synchronization between oscillators in regular and small-world networks, and find out the stable state of them in the kuramoto model. The results will compare with results of random and scale-free networks. It will be shown that, in random and scale-free networks, the only stable state is r=1 (fully synchronized state), mean while in regular, it has two stable state, r=1 and r=0. Moreover, we will introduce the new method for finding out the stable states in regular networks. In the old method we should calculate the huge matrix and its eigen values to recognize its stability, but in this method we can find out it, just from the phase of nodes. In small-world network we could see that, it has multi stable states with order parameter between one and zero. The result of this unusual aspect was the presence of some clusters in small-world. It means some nodes will not became synchronized like others; and make some groups and clusters in network. Then we investigate this work in the presence of white noise. We show that for a fix coupling constant, the robustness of the globally synchronized state against the noise is depend on the noise intensity in all three networks. At low noise intensities small-world network is more robust against loosing the coherency than random, and random is more robust than scale-free, but upon increasing the noise, the situation is vice versa. More than it we find out "stochastic synchronization" in small-world, which means that noise will help the system to be more synchronized in some range of its intensities. After this, we will investigate the reason of this phenomenon and we will use some methods like "clusters" to find out the reason. At the end we will find out the parameters that lead the network to have stochastic synchronization aspect; and we will see how the ranges of phase are important.