An ab initio study of structural, electronic, elastic, and dielectric properties of KMgF3 in cubic perovskite structure is presented in the framework of density functional theory. The calculations presented here employ generalized gradient approximation with projector augmented wave method. The fully relaxed structural parameters are found to be in reasonable agreement with available experimental data and with previous theoretical work. The independent elastic constants of cubic KMgF3 are derived from the derivative of total energy as a function of lattice strain in full detail. The bulk modulus and its first pressure derivative are obtained by fitting total energy versus volume data to a Murnaghan equation of state. The electronic band structure, total density of states, and projected density of states on each of the K, Mg, and F atoms are calculated and found to be in good agreement with previous theoretical results. First principles computed phonon dispersions for the cubic KMgF3 are reported for the first time. The imaginary part of frequency-dependent dielectric function is determined by summing over all possible transitions from occupied to unoccupied states and taking the appropriate transition matrix element into account. The Born effective charges computed by linear response within density functional perturbation theory are used together with the mode eigenvectors to decompose the lattice dielectric susceptibility tensor into contributions arising from individual IR-active phonon modes. Our results for the static and optical dielectric constant are in good agreement with previously reported experimental results.