Half-Heusler alloys are among the most promising thermoelectric materials for medium- and high-temperature waste heat recovery applications. This study investigates the physical properties of Half-Heusler compounds XBrH, with X = Sr, Ca, and Mg. We explored the structural, electronic, optical, and thermoelectric properties of these compounds using density functional theory (DFT) as implemented in the Wien2k package. The Generalized Gradient Approximation (GGA) as proposed by Perdew-Burke-Ernzerhof (PBE) and the modified Becke-Johnson (mBJ) functional were employed to calculate the exchange-correlation interactions. After doing structural optimization for a range of parameters, we discovered that the SrBrH compound is more stable than the CaBrH and MgBrH compounds. Our results show that the density of state calculations indicate semiconductor behavior for the XBrH with (X = Sr, Ca, and Mg) compounds. We also evaluated the real and imaginary parts of the dielectric tensor, the refractive index, the absorption coefficient, the electron energy loss, and the real and imaginary components of the optical conductivity, among other optical parameters. Additionally, we investigated the figure of merit (ZT), electronic and lattice thermal conductivity, Seebeck coefficient, and electrical conductivity. The MgBrH, CaBrH and SrBrH compounds showed p-type behavior, with positive values for the Seebeck coefficient and the greatest value of ≈180 μV/K, according to the thermoelectric data. At 1000 K, the ZT reach their highest values for CaBrH, SrBrH, and MgBrH, respectively, at 2.9, 2.8, and 0.9. The physical properties of the XBrH with (X = Sr, Ca, and Mg) compounds have been studied in detail.