This paper establishes the modulation transfer function （MTF） and signal-to-noise ratio （SNR） characterization models of the infrared array-aperture diffractive optical system based on the diffraction imaging mechanism. Subsequently， the imaging system diffraction efficiency is calculated based on the three-dimensional Finite Difference Time Domain （FDTD） method and the imaging characteristics are represented by combining the MTF and SNR. Finally， the effects of different working wavelengths， field of views and filling factors of the primary lens imaging characteristics are analyzed. The analysis results show that the diffraction efficiency， the MTF and SNR of infrared array-aperture diffractive optical system all have spectral and spatial variation characteristics， which reduce with the decrease of the primary lens filling factor. When the filling factor is 0.6， the integral area of MTF decreases by 45.42% and the SNR decreases by 4.92 dB compared with the ideal full aperture system. The established model can be used to characterize the imaging quality of infrared array-aperture diffractive optical system and provide reference to the imaging system design.