Using the phonon part of the effective Hamiltonian of Mishra and Tripathy (J Low Temp Phys, 75 (1989) 79), variation of pressure dependent zero-sound velocities has been studied. We have calculated the pressure dependent zero-sound velocities by using the contact interaction potential and pseudopotential of Aldrich and Pines. Our calculated values of pressure dependent zero-sound velocities are in a good agreement with the experimental data of Abraham and Osborue. By considering the effects of damping of the zero-sound mode, we have been able to explain satisfactorily the variation of zero-sound velocity with temperature T<1500 mK.