We can usually determine the pose of objects from three lines in a general position. The configuration of three non- coplanar lines that intersect at two points has some particular characteristics, which three lines in a general position do not have. Here, we present a new method of determining object pose using this particular line configuration. In theory, this method enriches the pose estimation methods from three line correspondences. In addition, it provides guidance for practical applications. Furthermore, we propose a method to deal with multi-solution phenomenon and a new iterative method. Simulation results demonstrate that our algorithm works speedily and robustly.