In this article, the structural phase stability of the KXP (X = Cr & Mo) compounds in the half-Heusler structure were investigated. The stability of the KXP compound was taken into account in the three phases α, β, and γ of the half-Heusler structure within various ferromagnetic (FM), antiferromagnetic (AFM), and nonmagnetic (NM) states. Total energy calculations, as well as cohesive energy calculations, indicated that for each KXP compound the β phase of the half-Heusler structure in the FM state has the lowest energy compared to the other phases α and γ. For all structural phases of the KMoP compound, the positive amount of the formation energy predicts that the compound cannot be grown in the hypothetical half-Heusler structure and prefers to decompose into stable phases of the constituent elements. The hull distance calculations justify that, unlike KMoP, the β and γ phases of the half-Heusler KCrP compound can be considered to be thermodynamically stable and suitable for experimental synthesis. Based on the elastic results, it can be argued that, unlike α phase, both β and γ phases of the KCrP compound in the FM state satisfy the conditions of mechanical stability. Moreover, γ phase of the KCrP compound is stiffer than β phase, while β phase has a more ductile nature compared to γ phase. In agreement with the elastic results, the phonon scattering calculations showed that both β and γ phases of the half-Heusler KCrP compound are dynamically stable and can be synthesized, while the α phase is regarded to be an unstable phase. The electronic calculations indicated that the KCrP compound in the different phases β and γ possess a half-metallic property with the highly desired Curie temperature, making it a potential candidate for use in spintronic devices.