Photoacoustic imaging, which combines the advantages of optical imaging and acoustic imaging, is a non-invasive imaging technique with high spatial resolution and high contrast ratio. Therefore, photoacoustic imaging is one of the research hot spots in biomedical imaging. However, the reconstruction of photoacoustic image is a typically ill-posed inverse problem. Aiming at the ill-posedness of photoacoustic imaging and the slow velocity of the reconstruction owing to the large size of the system matrix, we present a fast exponential-filtering reconstruction method based on Lanczos double diagonalization and the effectiveness of the proposed method is proved by numerical simulation. The simulation results show that the proposed method can increase the reconstruction velocity greatly, while preserving the high quality of reconstructed images. The reconstruction time is 1/67-1/47 of those using exponential-filtering method and back projection method.