The effect of grain size on the flow strength of FCC polycrystals was analyzed by means of computational homogenization. The mechanical behavior of each grain was dictated by a dislocation-based crystal plasticity model in the context of finite strain plasticity and takes into the account the formation of pile-ups at grain boundaries. All the model parameters have a clear physical meaning and were identified for different FCC metals from dislocation dynamics simulations or experiments. It was found that the influence of the grain size on the flow strength of FCC polycrystals was mainly dictated by the similitude coefficient K that establishes the relationship between the dislocation mean free path and the dislocation density in the bulk. Finally, the modeling approach was validated by comparison with experimental results of the effect of grain size on the flow strength of Ni, Al, Cu, and Ag.