Transition metal perovskite chalcogenides are attractive solar absorber materials for renewable energy applications. Herein, we present the first–principles screened hybrid density functional theory analyses of the structural, elastic, electronic and optical properties of the two structure modifications of strontium zirconium sulfide (needle–like α–SrZrS3 and distorted β–SrZrS3 phases). Through the analysis of the predicted electronic structures, we show that both α– and β–SrZrS3 materials are direct band gaps absorbers, with calculated band gaps of 1.38, and 1.95 eV, respectively, in close agreement with estimates from diffuse–reflectance measurements. Strong light absorption in the visible region is predicted for the α– and β–SrZrS3, as reflected in their high optical absorbance (in the order of 105 cm−1), with the β–SrZrS3 phase showing stronger absorption than the α–SrZrS3 phase. We also report the first theoretical prediction of effective masses of photo-generated charge carriers in α– and β–SrZrS3 materials. Predicted small effective masses of holes and electrons at the valence, and conduction bands, respectively, point to high mobility (high conductivity) and low recombination rate of photo-generated charge carriers in α– and β–SrZrS3 materials, which are necessary for efficient photovoltaic conversion. Density functional theory (DFT) theoretical simulation datasets are available in the .xlsx format (can be viewed either by MS Office or Libre Office) comprising 7 datasheets named according to their contents. Data for the optimized structures for the bulk alpha and beta SrZrS3 materials are available in CONTCAR format of the VASP simulation program. Volume vs Energy is provided for both phases; the band structure data (1st column is KPOINTS and the 2nd is Energy); the density of states (DOS) data are in 2 columns: first column been the Energy (eV) and the second column being the intensity of the DOS (arb. units). The optical absorbance, reflectivity, and refractive index data are also provided. All data can be plotted using any plotting software, e.g., xmgrace, excel.