Strontium molybdate (SrMoO3) thin films are grown epitaxially on strontium titanate (SrTiO3), magnesium oxide (MgO), and lanthanum aluminate (LaAlO3) substrates by pulsed laser deposition and possess electrical resistivity as low as 100 µΩ cm at room temperature. SrMoO3 is shown to have optical losses, characterized by the product of the Drude broadening, ΓD, and the square of the plasma frequency, ωpu2, significantly lower than TiN, though generally higher than Au. Also, it is demonstrated that there is a zero-crossover wavelength of the real part of the dielectric permittivity, which is between 600 and 950 nm (2.05 and 1.31 eV), as measured by spectroscopic ellipsometry. Moreover, the epsilon near zero (ENZ) wavelength can be controlled by engineering the residual strain in the films, which arises from a strain dependence of the charge carrier concentration, as confirmed by density of states calculations. The relatively broad tunability of ENZ behavior observed in SrMoO3 demonstrates its potential suitability for transformation optics along with plasmonic applications in the visible to near infrared spectral range.