Spherical Delaunay triangulation (SDT) which is a powerful tool to represent, organize and analyze spherical space data has become a focus of spherical GIS research. Projection stitching algorithm is one of the main construction algorithms of SDT. The basic idea of stitching algorithm is that the sphere is divided into two hemispheres to avoid projected image point coincidence. So, the practicality of projection stitching algorithm is lower because of merging two hemispheres. Aimed at the disadvantage of projection stitching algorithm, this paper puts forward a new algorithm to construct SDT used perspective projection principle. The projection center is placed on sphere to establish one-to-one mapping between spherical space points and plane image points. Experiment shows that the time complexity of our algorithm depends on Delaunay triangulation construction algorithm of the plane.