The trajectory planning of kinematically redundant manipulator is a key area of research that requires efficient optimization algorithms. This paper presents a new method that combines multiple objectives for the trajectory planning of robots with redundant degrees of freedom. The proposed technique combines Genetic Algorithm (GA) with a collision detection scheme to find the shortest and smoothest trajectory for a robot to move from a given initial point to a target location while avoiding obstacles. The evaluation function is based on the total linear displacement of end-effector and total angular displacement of joints with uniformity Cartesian and joint space velocities. The proposed approach is analyzed with three different working environments and the results indicated that the scheme can perform as well if not better than the collision detection and target finding method.