Based on the space optical communication link equation, it is given in detail that the signal-to-noise ratio (SNR) equations for the inter-satellite coherent optical communication receiving system (ISCOCRS) with different aberrations. With communication distance for 60000 km, transmission rate of 2 Gb/s binary phase shift keying (2PSK) homodyne geosynchronous orbit receiving system as an example, through numerical simulation, the effect of the tilt, defocusing, coma and astigmatism aberrations on the bit error ratio(BER) of the ISCOCRS is compared systematically. The simulation results show that effect of the tilt aberration is the BER is more seriously than the astigmatism when the different aberrations influence the ISCOCRS individually, at the same time, the different aberrations can be partly corrected by another when they effect mutually, Which leads to the lower BER. With the BER more than 10-6 as standard, through adjusting the tilt, the coma can be partly corrected when the normalized coma is more than 1.00, and adjusting the defocusing can partly correct the astigmatism when the normalized astigmatism is more than 0.53. Therefore, the aberrations′ influence should be overlooked in the process of designing the ISCOCRS. These results provide some theoretic basis for the ISCOCRS.