The discovery of infinite-layer nickelate superconductors has generated great enthusiasm for exploring new nickelate superconductors with higher Tc and further elucidating their superconducting mechanism. In this work, we systematically investigate the pressure effect on both normal state and superconductivity of La0.8Sr0.2NiO2 thin film by measuring resistance under various hydrostatic pressures up to 7.5 GPa. The results show that Tc exhibits a monotonic increase from Tconset ~ 19 K at ambient pressure to Tconset ~ 26 K at 7.5 GPa. Moreover, normal state resistance displays linear behavior in the measured pressure range, which is a hallmark of the strange metal state. The constructed temperature-pressure phase diagram reveals a potentially universal linear enhancement of Tc in infinite-layer nickelate superconductors at nearly optimal doping. This indicates that the evolution of Tc can be affected by multiple factors and can be further enhanced by pressure, epitaxial stress or substitution of rare earth metals. Our work provides critical insights for further enhancing Tc and constructing theoretical models to explore the superconducting mechanism in infinite-layer nickelate systems.