Solving the camera external parameters with single image space resection algorithm is a fundamental problem in the fields of photogrammetry and machine vision. Based on the previous work, a new robust algorithm is presented in this paper. A temporary coordinate system is created by three control points. Due to part of the coordinate component of these control points in the temporary coordinate system being zero, the resection solving is transformed to the solution of ternary quadratic equations, the initialize solutions for the nonlinear equations can be acquired by the image coordinates of the three points, which makes the solving process more reliable. In the experiment, 120 images of the control field are taken by the commercial industrial photogrammetry system and the external parameters are calculated with the proposed resection algorithm and the pyramid algorithm. Experimental results illustrate that the parameters calculated by the proposed resection algorithm are correct, and the convergence is good, showing that the proposed algorithm is suitable for solving external parameters of cameras with arbitrary rotation angles.