The composite samples of Al-alloy B95 reinforced with nanoparticles of a synthetic diamond have been fabricated by direct-melting the starting B95, adding the nanodiamond powder in the melt, and hashing it by an Ar-barbotage, followed by cooling and quenching. The linear and nonlinear elastic properties of the prepared samples have been investigated. The second order elastic constants (SOEC) have been determined on the basis of the measured sound velocities and densities of the samples. The data on the sound velocities of the longitudinal VL and transverse VT waves were obtained with an accuracy of ~1%; the elastic modules ~2-3%. For a quantitative characterization of the nonlinear elastic properties of a material, we measured the third order elastic constants (TOEC) of the composite samples by using a Thurston-Brugger method. Some relative changes of the elastic waves velocities in the tested samples from magnitude of the homogeneous uniaxial stress applied to it have been measured experimentally. The measurements have allowed to determine all independent TOEC C111, C112, C123. A relative comparison of the TOES data for B95/Nanodiamond composite with the data for the starting B95-alloy is made and discussed.