The Goal Oriented Recursive Path-Planning (GORP) algorithm described in this paper is a sensor based technique for navigating a holonomic mobile robot in an unknown environment, cluttered with convex and simple non-convex objects. This method tries to find the longest straight path segment with predetermined clearance from the obstacles in the direction that takes the robot closer to the goal or leads to get around the obstacle. Unlike other methods which try to be as far from the obstacles as possible, this method keeps only a safe distance from the obstacle in the way. This results in a shorter path which reduces the chance of confronting a new obstacle while keeping the path found safe enough. GORP guarantees to find a path in an open area and in a convex region cluttered with convex and simple non- convex objects if one exists.