This paper presents an improved time invariant path planning algorithm for autonomous underwater vehicles (AUV) in 3D space for generating smoother vehicle turn during course change at waypoints. The main purpose of this paper is to propose a simple and elegant algorithm by improving one of the basic guidance schemes. The waypoint guidance by line-of-sight (LOS) method has been modified here for correcting the reference orientation in 3D space to achieve smooth turn during course change. The orientation correction is performed by correcting both azimuth and elevation angles in spherical coordinates and then the desired orientation is calculated from the reference and correction angles. The path points are regularly parameterized in spherical coordinates and mapped to Cartesian coordinates. In order to achieve minimal calculation and smoother vehicle path in turns at waypoints, a threshold distance is defined in the direction of the waypoints. The proposed algorithm is computationally simple and can be used for both on-line and off-line mission planning. Also it can be integrated in any one of the modes with other guidance schemes such as obstacle avoidance algorithm. The details of the algorithm and simulation results are presented.