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.　©　2018,　Chinese　Lasers　Press.　All　right　reserved.