We have executed ab initio pseudopotential calculations on the structural, electronic, elastic, mechanical, vibrational, and electron-phonon interaction properties of hexagonal ZrRuP (h-ZrRuP) and orthorhombic ZrRuP (o-ZrRuP). The electronic states of both phases near the Fermi energy are found to be dominated by the d electrons of transition metal atoms, suggesting that they play a more active role in the generation of superconducting state for both phases of ZrRuP. A critical assessment of their elastic and mechanical properties reveals that the lattice of h-ZrRuP is softer than that of o-ZrRuP. A comparison of phonon dispersion curves for both phases indicates that the lower transverse acoustic branch of h-ZrRuP is much softer than that of o-ZrRuP. The soft character of this phonon branch gives rise to strong electron-phonon interaction in h-ZrRuP. Therefore the electron-phonon coupling parameter for h-ZrRuP equals to 1.25 which is considerably larger than the corresponding value of 0.57 for o-ZrRuP. As a consequence, phonon and electron-phonon interaction properties are crucial in making superconducting transition temperature much higher for h-ZrRuP than o-ZrRuP. At the end, the value of this temperature is found to be 12.49 K for h-ZrRuP and 3.89 K for o-ZrRuP which coincide with their experimental values of 12.93 and 3.82 K.