In the present study, we performed theoretical investigations to understand the origin of the half-metallic properties of new types of equiatomic quaternary Heusler compounds XFeCrAl (X = Rh, Pd, and Pt) and their possible applications in spintronics. These compounds crystallize in the Y-type structure with the F-43m space group, where the constitutive atoms are located in their non-equivalent positions in Type-I. Furthermore, we verified the thermodynamic, chemical, mechanical, and dynamical stabilities of these alloys. The results showed that they are stable in the magnetic phase where the optimized lattice constants are X-dependent. Among the three sample alloys, PdFeCrAl was shown to be the hardest with a brittle nature, whereas the others were found to be ductile. Analyses of the energy bands and magnetic profiles indicated the 100% spin-polarized, half-metallic, ferromagnetic natures of PdFeCrAl and PtFeCrAl, with EHM values of 0.09 eV and 0.03 eV, respectively, whereas RhFeCrAl is a nearly half-metallic ferrimagnet with 91% spin-polarization and it tends to act as a half-metal under the effect of uniform pressure. Their half-metallic nature can be expected because of the wide range of uniform strain due to their high bulk moduli. Thus, they have novel characteristics with lattice constants in the ranges of 5.55–5.64 Å, 5.53–6.04 Å, and 5.55–5.99 Å for RhFeCrAl, PdFeCrAl, and PtFeCrAl, respectively. The total magnetic moments of 1.98 μB, 2.99 μB, and 3.0 μB per formula unit obtained for RhFeCrAl, PdFeCrAl, and PtFeCrAl follow the Slater–Pauling rule. The highest Curie temperature (1113 K) obtained for PtFeCrAl demonstrates its feasible applications in spintronics with a high temperature limit.