One of the key techniques in the research of human motion analysis is the reconstruction of human spatial motion, which utilizes the anatomic points positions that can uniquely define the position and orientation of all anatomical segments. In this paper, upon the basis of Direct Linear Transform (DLT) and a human biomechanical model, the method to reconstruct human motion from an image sequence shot by a single stationary camera was described. In this method, the Lagrange Multiplier Method was used to minimize the difference between the actual and reconstructed length of limbs. This approach here is more comprehensive than previous methods that utilized cost functions to select results from feasible solutions. To examine this method, a practical human motion measured by a motion analysis system was selected and reconstructed. The spatial positions of joints were predicted with an average R2 of 0.9722 and mean residual error of 0.0022 m. This approach presented here provides a simple way to reconstruct the human spatial motion only utilizing a single camera.