After analyzing the feature of open surfaces, simple close surfaces and multiple connected close surfaces, a 3D triangulation algorithm which doesn t need partition the surface is proposed in this paper. In the 3D triangulation process, the triangular net spreads from the boundary of triangulated field to untreated field, and finally covers the whole surface. This algorithm can apply to the scattered data points on open surfaces, simple close surfaces and multiple connected close surfaces. The experimental results show that this algorithm can satisfy foundation for the surface reconstruction in the next step.