A theoretical study of structural, electronic, elastic and phonon properties of NaZnX (X = P, As and Sb) compounds is presented by performing ab initio calculations based on density-functional theory using the full-potential linear augmented plane wave (FP-LAPW) and pseudopotential plane wave method. The generalized-gradient approximation (GGA) and the local density approximation (LDA) are chosen for the exchange-correlation energy. The Engel-Vosko (EVGGA) formalism is applied for electronic properties. The calculated structural parameters, such as the lattice constant, bulk modulus, second-order elastic constants, the electronic band structures and the related total density of states and charge density are presented. The high-pressure alpha or beta phase of all compounds is investigated and phase transition pressure from tetragonal to high-pressure phase is determined. We have found that the Nowotny-Juza compounds NaZnP and NaZnAs are direct gap semiconductor at ambient pressure. Our calculations predict that NaZnSb is a metal in all phases. The bonding character and the phase stability of NaZnX (X = P, As and Sb) compounds are discussed. The nature and the size of the band gap of NaZnX (X = P, As and Sb) compounds are associated with the bonding character of two kinds of bonds, namely, Na-X and Zn-X bonds. The elastic constants were derived from the stress-strain relation. Phonon-dispersion curves were obtained using the first principles linear-response approach of the density functional perturbation theory. The influence of the pressure and X atomic number on the electronic structure, structural properties and phonon properties are investigated. (C) 2014 Elsevier B.V. All rights reserved.