To study the influence of desert sand on the frost resistance of concrete, the compression strength experiment of desert sand concrete after freezing and thawing test was carried out by rapid freeze-thaw method. The stress-strain curves and failure characteristics of desert sand concrete after different freeze-thaw cycles were obtained. The variations of surface damage characteristics, mass loss rate, dynamic elastic modulus loss rate, and ultrasonic wave velocity loss rate of desert sand concrete were analyzed. Experimental results show that with the increase of the number of freeze-thaw cycles, the mass loss rate of desert sand concrete had little change; the dynamic elastic modulus loss rate, ultrasonic wave velocity loss rate, relative peak strain, and ultimate strain increased; the relative peak stress and transverse deformation coefficient declined; the elastic modulus increased firstly and then decreased. With the same number of freeze-thaw cycles, the dynamic elastic modulus loss rate, ultrasonic wave velocity loss rate, and relative peak strain of desert sand concrete were less than those of ordinary concrete. However, the relative peak stress, transverse deformation coefficient, and elastic modulus of desert sand concrete were higher than those of ordinary concrete. On the basis of the uniaxial compression constitutive model of concrete put forth by Guo Zhenhai, the equation of stress-strain full curves was formulated. The influence of freeze-thaw cycles on the control parameters of stress-strain curves was analyzed, which can be applied for the frost resistance analysis of desert sand concrete structures.