The grain size dependence of the strain rate sensitivity (SRS) of copper were systematically investigated via tensile deformation at strain rates of ~10−4 s−1 and ~103 s−1. In contrast to the general perception that SRS increases with decreasing grain size at low strain rates in FCC metals, the SRS increases monotonously with grain size under deformation at high strain-rates of ~103 s−1. Analytical formulation based on the Nemat-Nasser-Li (NNL) and Modified-Rusinek-Klepaczko (MRK) models was established to reveal the essential dependence of SRS on grain size, at the change of strain rate: that the opposite dependence of SRS on grain size at low vs high strain rates can be attributed to the transformation of the dominant rate-controlling deformation mechanism from thermal activation at low strain rates to viscous drag at high strain rates. It is demonstrated that the thermal activation component of SRS, m*, which is nearly strain rate independent, increases with reducing grain size; while the viscous drag component of SRS, mvs, which is enhanced significantly at high strain rates, decreases with reducing grain size. Microstructural observation based on local misorientation characterization and statistics confirms that the viscous-drag dominates at high strain-rate deformation, and becomes progressively influential as grain size increases. This unveils the essence of viscous drag in the opposite grain size dependence of SRS at low vs high strain rates.