First principles calculations were carried out on the SrMoO4 compound which has been of interest owing to its technologically important physical properties. The structural, electronic, optical and thermal properties of this compound have been investigated under low pressure (LP) through the full potential linearized augmented plane wave method (FP-LAPW) within the framework of density functional theory. It is found that the phase transition from zircon to scheelite type structure occurs at negative pressure. The calculated ground state properties in scheelite structure are found to be in good accord with previously published data. Using the recently developed Tran Blaha-modified Becke Johnson approach, we have also studied the electronic band structure of this compound which shows the semiconducting behavior with a direct band gap of 4.30 eV in the scheelite phase, whereas the band gap is found to be 2.18 eV in the zircon phase. Various thermodynamic properties including the thermal volume expansion coefficient and heat capacities at constant volumes and pressures were calculated via the quasi-harmonic Debye model at different temperatures (0-1000 K). Furthermore, optical properties such as complex dielectric function, refractive index, and reflectivity spectra of the titled compound were studied for incident electromagnetic waves in an energy range up to 16 eV. The contributions to various transitions peaks in the optical spectra are analyzed and discussed with the help from the energy dependent imaginary part of the dielectric function.