The pressure dependencies of the magnetic and superconducting transitions, as well as that of the superconducting upper critical field, are reported for single crystalline EuRbFe 4 As 4 . Resistance measurements were performed under hydrostatic pressures up to 6.21 GPa and in magnetic fields up to 9 T. Zero-field-cooled magnetization measurements were performed under hydrostatic pressures up to 1.24 GPa under 20 mT applied field. Superconducting transition temperature, T c , up to 6.21 GPa and magnetic transition temperature, T M , up to 1.24 GPa were obtained and a pressure-temperature phase diagram was constructed. Our results show that T c is monotonically suppressed upon increasing pressure. T M is linearly increased up to 1.24 GPa. For the studied pressure range, no signs of the crossing of T M and T c lines are observed. The normalized slope of the superconducting upper critical field is gradually suppressed with increasing pressure, which may be due to the continuous change of Fermi velocity v F with pressure.