The perspective-three-line ( P3L) problem means using three straight lines and their 2D-3D corresponding relation to measure camera position and attitude parameters，which is a typical problem in monocular vision systems. Generally，P3L problem has multiple solutions． In this paper a special case of P3L problem is studied， in which the three lines are placed as a Z shape. It is proved that under this condition the number of problem solutions depends on the location of the camera optical center relative to the three lines． When the optical center locates in a special area the problem has unique solution． This result is very useful for pose determination using straight line features in many engineering applications. This paper also gives the method for finding the closed form solution of the problem in this condition. The experiment results verify the correctness of the conclusion.