The total energy and bulk properties of Fe₃AlX (X=B, C and N) with anti-perovskite structure at T=0 K were calculated by using the projector augmented-wave (PAW) approach within generalized gradient approximation (GGA) and local density approximation (LDA). The lattice constant, bulk modulus and its pressure derivative, elastic constants, shear modulus, Poisson's ratio and Debye temperature both in paramagnetic and ferromagnetic states for Fe₃AlX have been calculated. The calculations indicate that the ground states of Fe₃AlB and Fe₃AlC are ferromagnetic, while for Fe₃AlN its ground state is paramagnetic. The calculated total energy within LDA is lower than that within GGA. The calculated lattice constant of Fe₃AlC within GGA is in good agreement with experimental value, and this indicates that the calculations from GGA are more accurate than those from LDA. The calculated elastic constants and bulk moduli agree with other theoretical results available. The average magnetic moments of Fe in Fe₃AlX (X=B, C and N) are 1.483, 1.103 and 0.0 μ_B (GGA), or 1.300, 0.401 and 0.0 μ_B (LDA), respectively.