Ab initio computations are performed to study the structural, elastic, electronic, and vibrational characteristics of the cubic antiperovskite compound PbNCa3 under pressure up to 50 GPa. By using the generalized gradient approximation (GGA), the equilibrium structural parameters, energy band structure, density of states, elastic properties, and phonon frequencies for PbNCa3 have been examined. We have obtained some concerned feature as Young modulus and Poisson ratio for this compound using the elastic parameters. The computed elastic constant values show that PbNCa3 is stable up to 30 GPa as mechanically. To assess the stability of this compound dynamically, we have investigated the one-phonon DOS and phonon dispersion relations under pressure. Our results indicate that the calculated structural parameter values at 0 GPa are in accord with the existing data.