The crystal structure and elastic properties of chromium tetraboride ( CrB4 ) were investigated by pseudopotential plane-wave methods within the Perdew-Burke-Ernzerhof ( PBE) form of generalized gradient approximation ( GGA). The calculated equilibrium structural parameters of Pnnm-CrB4 are in good agreement with the available experimental data and other theoretical results. Moreover, the elastic constants Cij, bulk modulus B, shear modulus G and elastic modulus E under high pressure were calculated, and the toughness and brittleness of Pnnm-CrB4 under high pressure were analyzed with the Poisson ratio σ and B/ G. To study the elastic anisotropy of Pnnm-CrB4 in detail, the anisotropic factors A1 ,A2 ,A3 for shear and Ba , Bb, Bc for the directional bulk modulus were also calculated. The Vickers hardness HV of Pnnm-CrB4 was estimated at the same time. Finally, the total and partial density of states of Pnnm-CrB4 under high pressure were studied so as to have a better understanding of the mechanical and elastic properties of Pnnm-CrB4 .