According to the First Principle based on Density Functional Theory (DFT), dopting the plane wave pserdopotential method in which the Local Density Approximation (LDA) and Generalized Gradient Approximation (GGA) were used respectively, the electronic structuresand the elastic constants of RhZr2 alloy with tetragonal system were calculated. The internal positions of atoms in the unit cell were optimized and the ground state properties such as band structure, density of state, charge densities difference, cohesive energies and the enthalpies of formation were calculated. The results show that the elastic constant C11, C12, C13, C33, C44 and C66 of tetragonal RhZr2 are 195.38, 176.80, 109.00, 235.65, 11.12 and 24.51 GPa, respectively, and the bulk modulus is 156.92(±2.22) GPa, the Young’s modulus is 34.77, 34.77 and 171.80 GPa for [100]、[010] and [001] directions, the shear modulus Gxy, Gzx, Gzy of RhZr2 is 24.79、14.57 and 19.68 GPa, respectively.