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-cool magnetization measurements were performed under hydrostatic pressures up to 1.24 GPa under 20 mT applied field. Superconducting transition temperature, $T_text c$, up to 6.21 GPa and magnetic transition temperature, $T_text M$, up to 1.24 GPa were obtained and a pressure-temperature phase diagram was constructed. Our results show that $T_text c$ is monotonically suppressed upon increasing pressure. $T_text M$ is linearly increased up to 1.24 GPa. For the studied pressure range, no signs of the crossing of $T_text M$ and $T_text c$ 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.
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