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A crossover behavior in the initial creep stage during nanoindentation with a constant load for a high-entropy-based alloy CoFeNi is found. The holding time and stress in the indentation tests are evaluated to reveal the intrinsic mechanism of the crossover point. It indicated that the initial creep behavior is dominated by the strain-hardening at the beginning and then transit into the dislocation migration induced viscous stage. The transition presents the crossover, where the strain hardening effect predominates in a very short initial period while the viscous stage accounts for most of the initial creep stage with a time-dependent strain rate.