Parking path planning is an essential technology for intelligent vehicles. Under a confined area, a parking path has to guide a vehicle into a parking space without collision. To realize this technology, circle-based planning algorithms have been studied. The main components of these algorithms are circles and straight lines; subsequently, the parking path of the algorithm is designed by the combination of these geometric lines. However, the circle-based algorithm was developed in an open space within an unlimited parking lot width, so a feasible path cannot always be guaranteed in a narrow parking lot. Therefore, we present a parking planning algorithm based on Turning Standard Line (TSL) that is a straight line segment. The algorithm uses the TSL lines to guide sequential quadratic Béizer curves. A set of these curves from parking start to goal position creates a continuous parking path. Although the size of free space in a parking lot is small, iterative TSL guides Béizer curves to draw a feasible parking path. We use a sampling technique to find the optimal path and select the minimum-cost path. The planning algorithm proposed in this paper is verified by simulation in various-size parking environments. The simulation results show that the generated path by this algorithm is adapted to the narrow width of a parking lot.