The creep behavior of nanocrystalline Cu with an average grain size of 25 nm was investigated by nanoindentation test at room temperature. Using the creep strain rate versus creep stress data obtained at different loading rates, the activation volume and strain rate sensitivity were determined obtained by cooperating the continuous stiffness measurement (CSM) technique. The results showed that the activation volume first increases and then decreases, and the strain rate sensitivity first decreases and then increases with increasing the creep stress. The experimental activation volume and strain rate sensitivity versus the creep stress data exhibit very good agreements with the theoretical values calculated by the previous models, respectively. The analysis based on the data of the activation volume and strain rate sensitivity revealed that at lower stress, the grain boundary activities dominate and lead to the lower creep strain rates; at higher stress, the dislocation activities dominate and lead to the higher creep strain rates. The analysis based on the data of the nanoindentation test also revealed that the use of the CSM technique can lead to the continuous creep strain rate versus creep stress data, which allows us to uncover the creep mechanisms over a wide range of the creep stress from the initial to steady stage.