A GPU-based spectrum reconstruction algorithm is proposed and realized aiming to meet the need for real-time spectral data processing. By analyzing the working principle and data property of snapshot Fourier transform imaging spectrometer and combining with CUDA data Parallel Processing Architecture, the article optimizes the reconstruction algorithm, including paralleling the reconstruction algorithm and optimizing the memory accessing, and implements parallel spectrum reconstruction algorithm. As a consequence, the spectrum reconstruction rate is extremely increased. The experimental results indicate that, compared with CPU serial algorithm, the GPU-based parallel spectrum reconstruction algorithm proposed in this article achieves the same reconstruction accuracy but around 25 times in computational efficiency. By taking advantage of GPU parallel computing, spectrum reconstruction efficiency is extremely improved which lays the foundation for the implementation of snapshot imaging spectrometer in real-time measurement.