Structural, electronic, magnetic, mechanical and lattice dynamical properties of XCoBi (X: Ti, Zr, Hf) Half-Heusler compounds have been investigated according to density functional theory and generalized gradient approximation. Among alpha, beta and gamma structural phases, gamma-phase structure has been found as the most stability characteristics depending on the calculated formation enthalpies, energy-volume dependencies and Cauchy pressures. Energy-volume plots of possible magnetic orders of gamma-phase XCoBi compounds have been analyzed and the most stable order has been found as paramagnetic nature. The theoretical studies on gamma-phase structures resulted in band gap energies of 0.96, 0.99 and 0.98 eV for TiCoBi, ZrCoBi and HfCoBi semiconducting compounds, respectively. Born-Huang criteria applied on elastic constants of interest compounds has indicated that gamma-phase is also mechanically stable for all studied compounds. In addition, various mechanical, lattice dynamical and thermodynamical parameters of XCoBi compounds have been calculated in the present study.