Based on the theory of the atom force model in magneto-optical trap, the sub-Doppler cooling mechanism is researched under the condition that the diffracted light in the grating magneto-optical trap is nonorthogonal to the magnetic field, and the theoretical models of atomic force cooling and trapping in four beam and five beam grating magneto-optical trap are established. The scattering force of atom under the condition of grating magneto-optical trap is calculated, and the influence of grating diffraction angle on atomic cooling velocity and atomic trapping range is analyzed. The results show that the resultant force of the diffracted light and the incident light is zero at the center of the magnetic field, forming an effective potential well. The change of the polarization component of the diffracted light caused by the diffraction angle of the grating has an impact on the damping force, the restoring force and the atomic trapping velocity of the atom, and will ultimately affect the number of atoms trapped in the grating magneto-optical trap. The theoretical study provides a theoretical basis for the realization of atomic cooling and trapping in the grating magneto-optical trap and the design of the grating chip.