The theoretical calculations on structural, half-metallic and elastic properties of FeZrX (X = P, As, Sb and Bi) half-Heusler compounds were investigated using WIEN2k code. In all compounds, the ferromagnetic (FM) phases in Type II structure are more stable energetically than non-magnetic (NM) phases. The spin-up electrons of all half-Heusler compounds have semiconducting nature with energy gaps while spin-down electrons have metallic behavior. FeZrM (M = III, IV and VIAgroup elements) compounds have also been investigated, but these compounds have metallic properties, whereas FeZrP, FeZrAs, FeZrSb and FeZrBi compounds have half-metal nature. According to calculatedCij elastic constants, FeZrX (X = P, As, Sb and Bi) half-Heusler compounds are elastically stable and these compounds are ductile materials. Finally, FeZrX (X = P, As, Sb and Bi) half-Heusler compounds were obtained true half-metal ferromagnetic materials (HMF) within 1.00 mu(B)/f.u.