Abstarct: The quantum walks in comparison to the classical random walks, have some major differences in the probability distribution, variance, diffusion velocity, etc. The localization phenomenon is one of the distinctive features of the quantum walks. This phenomenon is known as the probability of finding the walker in its initial position after long time walking. It has been demonstrated that the localization effect in the quantum walks can have potential applications for the quantum search algorithms. In this thesis, by focusing on the inhomogeneous one-dimensional quantum walks namely those have different coin operator for different spaces, we will investigate the localization probability by using a path counting approach..........