Heusler alloy is a widely studied spintronic material in recent years, which has played a huge role in the field of spintronic devices due to its high spin polarization and high Curie temperature. Using first-principles calculation to predict the basic properties of Heusler alloy can not only save experimental costs and time but also provide a reliable theoretical basis for experimental research. This study used a first-principles calculation to study the magnetic and mechanical properties of full-Heusler alloy Cr2ZrSi with an L21-type structure. The research results indicate that the alloy is a half-metallic ferromagnetic material with a theoretical value of 100% spin polarization. The magnetism mainly comes from the asymmetric spin contribution of d-orbital electrons of transition metal atoms and their hybridization. At the same time, this complex hybridization coupling process is also a possible reason for the half-metallic band gaps. In terms of mechanical properties, the Cr2ZrSi alloy exhibits good ductility and anisotropy, with a Debye temperature of 303.848K. Our theoretical research results provide more choices and theoretical basis for subsequent experimental research.