The radiation output characteristics of the Smith-Purcell free electron laser (S-P FEL) based on different sheet-beams are studied by the three-dimensional numerical simulation. As a sheet-beam flies closely to the rectangular gratings, it emits incoherent Smith-Purcell (S-P) radiation. The full feedback resonator reflects the radiation with a random azimuth angle back onto the sheet-beam and causes the electrons to be modulated, which leads to electron bunching and coherent S-P radiation. The numerical simulation results show that the power and power spectrum density of S-P FEL can be increased by the sheet-beams. The modulation of sheet-beam, the bunching state of sheet-beam, and the power and power spectrum density of S-P FEL, all increase with the increasing aspect ratio of sheet-beam.