The first-principles tight-binding linear muffin-tin orbital method within the local density approximation (LDA) has been used to calculate the ground-state properties, structural phase stability and pressure dependence of the band gap of NaZnX (X = P, As, Sb). All three compounds are found to crystallize in the tetragonal Cu2Sb-type (C38) structure. NaZnAs is also found to crystallize in the zinc-blende-type related structure, i.e.the MgAgAs (order CaF2)-type structure. By interchanging the position of the atoms in the zinc-blende structure, three phases (α, β and γ) are formed. The energy-volume relations for these compounds have been obtained in the Cu2Sb-type and cubic α, β and γ phases of the zinc-blende-type related structure. Under ambient conditions these compounds are more stable in the Cu2Sb-type structure and are in agreement with experimental observations. At high pressure, these compounds undergo a structural phase transition from the tetragonal Cu2Sb-type to cubic α (or β) phase, and the transition pressures were calculated. The equilibrium lattice parameter, bulk modulus and the cohesive energy for these compounds have also been calculated and are compared with the available results. In the Cu2Sb-type structure, NaZnP is found to be a direct-band-gap semiconductor, NaZnAs shows a very small direct band gap and NaZnSb is found to be a metal. In the α and β phases, NaZnP is found to be a direct-band-gap semiconductor, whereas NaZnAs and NaZnSb are found to be semi-metallic. In the γ-phase, all three compounds are found to exhibit metallic behaviour. However, this phase is energetically unfavourable. © 2008 IOP Publishing Ltd.