The pressure effect up to 24.0 kbar on superconducting and normal-state properties of β-Bi2Pd single crystal (Tc ≈ 4.98K at ambient pressure) has been investigated by measurements of the electrical resistivity. In addition, we have performed the heat capacity measurements in the temperature range 0.7–300 K at ambient pressure. The recent calculations of electronic density of states, electron-phonon interaction spectral function, and phonon density of states of β-Bi2Pd [Zheng and Margine, Phys. Rev. B 95, 014512 (2017)], are used to fit the resistivity and the heat capacity data. In the superconducting state we have focused on the influence of pressure on the superconducting transition temperature Tc and upper critical field Hc2 and a negative effect with dTc/dp = –0.025K/kbar and dHc2/dp = –8mT/kbar is found. A simplified Bloch-Grüneisen model was used to analyze the pressure effect on the temperature dependence of the normal-state resistivity. The obtained results point to a decrease of the electron-phonon coupling parameter λ and to a shift of phonon frequencies to higher values with pressure. Moreover, the temperature dependence of the normal-state resistivity follows a T² dependence above Tc up to about 25 K. Together with the enhanced value of Sommerfeld coefficient γ = 13.23 mJ mol⁻¹ K⁻² these results point to a certain role of the electron-electron interaction in the superconducting pairing mechanism in β-Bi2Pd.