We propose an algorithm that solves the perspective-n-point problem in the framework of variable projection. The perspective-n-point is the problem of determining the rotation and translation parameters of a camera, which is widely used in computer vision, photogrammetry, robotics, space rendezvous and virtual reality. We separately estimate the rotation and translation parameters in the variable projection framework. Firstly, an optimal rotation matrix is solved by using the Wahba problem with fixed translation parameters. By applying the formula for the derivative of the singular value decomposition, the derivative of the optimal rotation matrix is calculated with respect to the translation parameters, then the derivative of the objective function with respect to the translation parameters is obtained. Finally, the objective function is minimized by Levenberg-Marquardt algorithm over the translation parameters. The experimental results show that the proposed algorithm is one of the most accurate and effective algorithms and has a large convergence basin.