Pressure, as a thermodynamic parameter, has a significant influence on the solidification process of alloys, including the precipitation behavior of alloys. Based on this, a Ni35Al35Co5Cr20Cu5 high-entropy alloy (HEA) with a precipitated phase was designed in this study. Through a comprehensive investigation of the microstructure and properties of Ni35Al35Co5Cr20Cu5 HEAs solidified under ambient pressure (AP) and 7 GPa, we confirmed the influence of pressure on the precipitation behavior of the precipitated phase. The results indicate that the solidification microstructure of the AP alloy displays a diverse distribution of Cr-rich precipitated phases with varying sizes, ranging from approximately 40 nm to approximately 10 μm. It is also worth noting that as the size of the Cr-rich phase increases, it becomes closer to the grain boundary. However, under 7 GPa, the Cr-rich precipitated phases near grain boundaries disappeared, and heterogeneous precipitation (continuous and discontinuous precipitation) emerged. Meanwhile, the nanophase size decreases significantly to approximately 10 nm and achieves a more uniform distribution throughout the alloy. Moreover, the grains undergo significant refinement. Consequently, substantial improvements in both strength and plasticity are achieved.