The composition-dependent elastic properties and electronic structure of off-stoichiometric TiNi with a B2 structure are investigated by using the first-principles exact muffin-tin orbitals method in combination with coherent potential approximation and first-principles plane-wave pseudopotential method (for computing bonding charge densities). The Zener anisotropy, c 44 /c 0 , increases with increasing Ni contents, but is quite small, indicating a strong correlation between the softening of c 44 and c 0 with decreasing temperature during martensitic transformation (MT). For the Ni-rich TiNi, c 44 increases with increasing Ni content whereas c 0 decreases. On the Ti-rich side, both c 44 and c 0 are insensitive to the composition. It was observed that larger c 44 corresponds to higher MT temperature, and the composition dependence of elastic modulus is discussed on the basis of the bonding charge densities and electronic density of states. We propose that the strong composition dependence of the elastic modulus of the Ni-rich TiNi can be attributed to the Coulomb static electronic repulsion between the antisite Ni atoms and their surroundings. The insensitivity of the elastic modulus of the Ti-rich TiNi to the composition is due to the absence of such repulsion between the Ti antisites and their nearest neighbors.