In this paper, the first-principles study is performed to calculate the structural, electronic and phonon properties of alkali halides NaBr and NaI. The calculations for structural and electronic properties have been carried out using the full-potential linearized augmented plane-wave (FP-LAPW) method that is employed in the WIEN2k code, whereas the phonon properties are studied using the Quantum Espresso program based on density-functional theory within plane-wave fundamental sets and pseudo-potentials approaches. The calculation of structural, electronic band properties were carried out using generalized gradient approximation (GGA), local-density approximation (LDA) and a combination of modified Becke-Johnson exchange potential with LDA and GGA (TB-mBJ-GGA/LDA) for exchange-correlation potential. The calculated structural parameters are in good agreement with experimental results. In our electronic calculations, the obtained bandgaps are underestimated by LDA and GGA functionals compared to empirically derived results, which is an expected result. However, the calculated bandgaps by the modified Becke-Johnson exchange potential are in perfect agreement with the experiment. Finally, the dynamic properties of NaBr and NaI compounds were investigated. Both phonon dispersion and phonon density of states curves were calculated for compounds along with the high symmetry directions in the Brillouin region. The dynamical properties of NaBr and NaI crystals are analyzed and discussed.