The structural, mechanical, electronic, and bonding properties and phase transition of NaZnSb are explored using the generalized gradient approximation based on ab initio plane-wave pseudopotential density functional theory. With the help of the quasi-harmonic Debye model, we probe the Grüneisen parameter, thermal expansivity, heat capacity, Debye temperature, and entropy of NaZnSb in the tetragonal phase. The results indicate that the lattice constants and the bulk modulus and its first pressure derivative agree well with the available theoretical and experimental data. NaZnSb in its ground state structure exhibits a distinct energy gap of about 0.41 eV, which increases with increasing pressure. Our conclusions are consistent with the theoretical predictions obtained by the ABINIT package, but are different from those obtained through the tight-binding linear muffin-tin orbital method. As a result, further experimental and theoretical researches need to be carried out. For the purpose of providing a comparative and complementary study for future research, we first investigate the thermodynamic properties of NaZnSb.