A two-stage data-analysis method is proposed for total-reflection high-energy positron diffraction (TRHEPD). TRHEPD is a novel experimental method for the determination of surface structure, which has been extensively developed at the Slow Positron Facility, Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK). The data analysis is based on an inverse problem in which the atomic positions of a surface structure are determined from the experimental diffraction data (rocking curves). The relevant forward problem is solved by the numerical solution of the partial differential equation for quantum scattering of the positron. In the present two-stage method, the first stage is a grid-based global search and the second stage is a local search for the unique candidate for the atomic arrangement. The numerical problem is solved on a supercomputer.