Grating spectrometer is one of important tool to study the thermodynamics properties of the solar atmosphere with different height distributions, but its imaging performance will be limited by the wavefront aberration generated by atmospheric turbulence and optical system adjusting errors and so on, so daptive optics (AO) is needed to compensate the influence of the wavefront aberration. However, the traditional adaptive optics can not be directly applied in the grating spectrometer, since the tiny slit will filter the wavefront aberration to a certain extent. The influence of filter slit on the adaptive optics correction is studied. A differential correction method based on the sensitivity of the filter slit is proposed and the numerical simulation is conducted. The results show that after the adaptive optics correction, the spectral resolution is notably improved, and also the energy utilization η is considerably improved, better than 90% with a slit width of 3 times diameter of Airy spot.