We　propose　a　single-frame　zero-order-eliminated　reconstruction　method　by　fractional　Fourier　transform　filtering　for　an　off-axis　digital　hologram.　The　filtering　in　the　fractional　Fourier　transform　domain　of　the　hologram　can　effectively　improve　the　reconstruction　resolution,　but　it　is　required　to　remove　its　zero-order　term.　With　the　zero-order-term　elimination　of　the　Laplacian　hologram,　the　higher　reconstruction　resolution　of　a　single-frame　hologram　is　achieved　by　zero-padding　the　hologram　and　choosing　the　optimal　option　of　the　fractional-order　number.　The　results　demonstrate　that　the　resolutions　of　reconstructed　amplitude　and　phase　images　are　obviously　improved.　It　will　have　a　promising　application　in　real-time　imaging　for　biological　cells　and　moving　objects.　©　2023　Optica　Publishing　Group　under　the　terms　of　the　Optica　Open　Access　Publishing　Agreement.