Traditionally, we usually utilize the method of shotgun to cut a DNA sequence into pieces and we have to reconstruct the original DNA sequence from the pieces, those are widely used method for DNA assembly. Emerging DNA sequence technologies open up more opportunities for molecular biology. This paper introduce a new method to improve the efficiency of reconstructing DNA sequence using suffix array based on CUDA programming model. The experimental result show the construction of suffix array using GPU is an more efficient approach on Intel(R) Core(TM) i3-3110K quad-core and NVIDIA GeForce 610M GPU, and study show the performance of our method is more than 20 times than that of CPU serial implementation. We believe our method give a cost-efficient solution to the bioinformatics community.