We performed molecular dynamics simulations of ubiquitin with the distinct water models, TIP3P, SPC, SPC/E, and SPC/Fw, in different system sizes with different box shapes. The translational diffusion constants of pure water linearly depend on the effective box length, which is known as finite size effect, whereas the first and second rotational times of pure water are nearly constant. We then observed that both the overall translation and rotational motions of the protein are linearly correlated to the viscosity of pure water. As expected from the finite size effect in pure water, the translational diffusion of the protein is significantly affected by the system size, and rotational diffusion is nearly size-independent. After correction for the finite size effect, the SPC/E and SPC/Fw models reproduce both the translational and rotational motion of the protein relatively well. Thus, water models that reproduce the experimentally derived diffusional properties of pure water accurately are expected to also be suitable for simulating protein diffusion quantitatively.