In this work, we have theoretically investigated the band structure of antiperovskite chromium-based carbides and nitrides Cr3PX (X = C and N) using the first-principles calculation based on the FP-APW+LO method. The principal structural properties i.e., lattice constants (a,b,c) and internal parameters are in accordance with the experimental results. The calculated values of elastic constants indicated that the mechanical strength for both Cr3PC and Cr3PN compounds at (001) plane is higher than the (100) and (010) planes. Moreover, the Cr3PX compounds are expected to be hard materials with ductile nature. In addition, we have found that the FM ground state of herein materials Cr3PC and Cr3PN are energetically favorable with low magnetic moments of about 2.27 and 2.94 AB, respectively, confirming that these are weak ferromagnets. Based on the spin-polarized electronic band structure we have found that both alloys have metallic behavior, such behavior has been shown in the calculated electrical conductivity. We have also estimated other thermoelectric constants like the Seebeck coefficient, thermal conductivity, power factor and electrical resistivity of Cr3PC and Cr3PN compounds. (C) 2016 Published by Elsevier Ltd.