To solve the problem of path planning for parallel parking in narrow spaces, a two-piece five order polynomial equation based method was proposed for calculating approaching path and reverse path respectively, among which the approaching path was applied for adjusting the vehicle pose so that a curvature optimal path for reversing car into parking lot is available. Simulation was performed by considering the general size of parking lot and family car, as well as the kinematic model of vehicle motion, to find a collision free path in free space. The result shows that the two-piece five order polynomial equation-based method can realize intelligent parking in narrow spaces, and the steering angle of wheel changes continuously on the linked path.