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With the geometry, theory of errors and optimization principle used and the related national standard referred, a novel 3DLSA for evaluating the spatial straightness errors was proposed, so as to evaluate the spatial straightness errors effectively and to gain the error values with higher accuracy. Then,a mathematical model of the 3DLSA was deduced, true three-dimensional fitting of the spatial line was theoretically carried out. Finally, the 3DLSA was programmed, and the corresponding numerical experiments were done. The experimental results show that compared with the existed algorithms such as the algorithm of two endpoints linked-line, the least squares method（LSM）and other algorithms in evaluation of the spatial straightness errors, the 3DLSA is more effective and has better robustness and higher accuracy. 