The coarse-grained reconfigurable architecture (CGRA) is a promising computing platform that provides both high performance and high power-efficiency. The computation-intensive portions of an application (e.g. loop nests) are often mapped onto CGRA for acceleration. However, mapping loop nests onto CGRA efficiently is quite a challenge due to the special characteristics of CGRA. To optimize the mapping of loop nests onto CGRA, this paper makes three contributions: i) Establishing a precise performance model of mapping loop nests onto CGRA, ii) Formulating the loop nests mapping as a nonlinear optimization problem based on polyhedral model, iii) Extracting an efficient heuristic algorithm and building a complete flow of mapping loop nests onto CGRA (PolyMAP). Experiment results on most kernels of the PolyBench and real-life applications show that our proposed approach can improve the performance of the kernels by 27% on average, as compared to the state-of-the-art methods. The runtime complexity of our approach is also acceptable.