In this work, we present a novel algebraic method to the perspective-three-line (P3L) problem for determining the position and attitude of a calibrated camera from features of three known reference lines. Unlike other methods, the proposed method uses an intermediate camera frame F and an intermediate world frame E, with sparse known line coordinates, facilitating formulations of the P3L problem. Additionally, the rotation matrix between the frame E and the frame F is parameterized by using its orthogonality, and then a closed-form solution for the P3L pose problem is obtained from subsequent substitutions. This algebraic method makes
the processes more easily followed and significantly improves the performance. The experimental results show that the proposed method offers numerical stability, accuracy and efficiency comparable or better than that of state-of-the-art method.