With local geodesic line as a supplement, this paper proposes an improved fixed-angle initial path planning algorithm on grid surfaces. This algorithm avoids the no-solution and multi-solution situations of the traditional parametric methods, and is especially suitable for complex curved surfaces and spliced surfaces with large curvature changes. After the uniform coverage is obtained by equidistant offsetting algorithm, two boundary processing ideas are presented to solve the problem that the offsetting paths cannot reach the surface boundary. The algorithm is verified on a wing model and the visualization is realized in CATIA's reverse engineering module. The validation shows that the proposed algorithm is reliable, systematic and adaptable, and has engineering application value.