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 alpha, beta and gamma 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 beta phase of the half-Heusler structure in the FM state has the lowest energy compared to the other phases alpha and gamma. 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 beta and gamma 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 alpha phase, both beta and gamma phases of the KCrP compound in the FM state satisfy the conditions of mechanical stability. Moreover, gamma phase of the KCrP compound is stiffer than beta phase, while beta phase has a more ductile nature compared to gamma phase. In agreement with the elastic results, the phonon scattering calculations showed that both beta and gamma phases of the half-Heusler KCrP compound are dynamically stable and can be synthesized, while the alpha phase is regarded to be an unstable phase. The electronic calculations indicated that the KCrP compound in the different phases beta and gamma possess a half-metallic property with the highly desired Curie temperature, making it a potential candidate for use in spintronic devices.