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Considering the impact of chemical compositions, the mechanical properties and microstructure evolution of the single-crystal FCC CoCrFeNi-based high-entropy alloys (HEAs) are investigated by using molecular dynamics simulation in nanoindentation. The addition of Cu and Mn elements would decrease the stacking faults energy resulting in the dislocation-mediated deformation. Moreover, the total number of chemical compositions of CoCrFeNi-based HEAs has critical effects on the results according to the Hertz contact theory. The plastic deformation is studied by correlating the P–h curve with the instantaneous defect structure and dominated by nucleation of Shockley partial dislocations or the motions of stacking faults. Owing to the large amount of Hirth and Stair-rod dislocations, CoCrFeNiCu HEA has the largest indentation force, next followed by CoCrFeNi and CoCrFeNiMn HEAs. Then, the influence of chemical composition on the radial distribution function is explored, and it exhibits that Cu and Mn elements are conducive to amorphization. Finally, the analysis of microstructure evolution reveals that the Mn addition would contribute to the slipping process for CoCrFeNi-based HEAs causing the decrease of indentation force and hardness. In contrast, the Cu addition results in irregular slipping mode accompanying the appearance of dislocation loops. In this simulation, the mechanical properties of single-crystal CoCrFeNi-based HEAs are strongly dependent on the chemical composition, which contributes to the composition design of high entropy alloys in the future.