Aiming at the stereo matching problem in digital speckle projection 3D measurement technology, a semi-global stereo matching algorithm based on Inverse Compositional Gauss-Newton iterative algorithm is proposed.The algorithm uses the matching cost value based on the Census transform to measure the similarity between pixels, and the cost aggregation algorithm enhances the robustness of the matching cost to noise;On this basis, a reverse synthetic Gauss-Newton algorithm based on the first-order shape function is proposed to achieve sub-pixel parallax optimization;Finally, an erroneous parallax elimination algorithm coupled with uniqueness check, left-right consistency check and connected region constraints is proposed to eliminate the erroneous parallax caused by occlusion and noise. Experimental results show that the algorithm can accurately, densely and completely reconstruct the three-dimensional topography of complex objects, and the reconstruction accuracy is better than 0.06mm.