High resolution synthetic aperture radar (SAR) generates mass data, which results in huge computational load. Complex approximate message passing (CAMP) is a kind of sparse reconstruction algorithms with fast convergence speed, so it is often used for sparse signal reconstruction. To solve the problem of huge computational load, this paper presents a parallel algorithm based on CAMP and optimizes Chirp Scaling operator and sorting of CAMP on compute unified device architecture (CUDA）. We mainly optimize matrix transpose, FFT and IFFT in Chirp Scaling operator, and introduce parallel version bitonic sorting. Finally, we reconstruct point targets by serial CAMP algorithm and parallel CAMP algorithm respectively. The experiment results demonstrate that, parallel CAMP algorithm is faster (up to 29.55 times) than serial CAMP algorithm on the basis of correct reconstruction.