An autonomous vehicle has to understand the surrounding dynamic environment to make the driving decisions such as lane change by giving way to the dynamic obstacles. Motion planning is a challenging problem for an autonomous vehicle while changing a lane in the complex dynamic environment, as the optimal solution for routing must be computed in real time. This thesis provides a framework for an autonomous vehicle to analyse the lane change possibilities. Information from the digital map and estimation of the surrounding objects evaluate a method to find the trajectory for a lane change. The method involves constrained optimization problem of trajectory planning by incorporating interpolated optimal route as the sampling points. Numerical simulations show the effectiveness of the proposed technique in a scenario emulating a driving context for the autonomous vehicle. The result shows that, in a complex dynamic environment, the innovation of deploying model of the road descriptions, graph search and trajectory planning together makes the proposed method far better than the other methods applied in the researches done before for the lane change.