Mechanical properties of aeolian sand concrete, are important indicators to characterize the performance of aeolian sand concrete. Domestic and foreign scholars have extensively studied the cubic compressive strength, splitting tensile strength and microscopic mechanism of aeolian sand concrete, but there are few researches on the mechanical properties of concrete under axial compression, while the compression of concrete prism is closer to the engineering practice. Therefore, 10 groups of aeolian sand-fly ash concrete were prepared by mixing aeolian sand (replacement rate was 0~40%) and fly ash (replacement rate was 10%~20%) with river sand and cement of equivalent quality. The 60-day-old aeolian sand-fly ash concrete axial compression test was carried out, and the axial compression failure morphology, microstructure, stress-strain relationship, axial compressive strength, peak strain, elastic modulus and Poisson’s ratio of the aeolian sand-fly ash concrete were tested. It was found that the stress-strain curves of aeolian sand concrete with different amounts of aeolian sand in the elastic stage are basically consistent. After entering the elastic-plastic stage, the stress of aeolian sand concrete increases faster than that of the reference concrete, and the brittleness of concrete increases. The axial compressive strength, elastic modulus and Poisson’s ratio showed a trend of increasing first and then decreasing with the increase of aeolian sand content, and decreased with the increase of fly ash content. Finally, the constitutive parameter A of the rising section of Guo Zhenhai’s classic model was subjected to secondary evolution, and an evolution model between the constitutive parameter and axial compressive strength and aeolian sand content was established. The constitutive equation of the stress-strain rising section of aeolian sand concrete was obtained. The calculation model had certain reference for the research and application of aeolian sand concrete.