Nonstatic nuclear potential due to one-pion-exchange process is derived in the momentum space without using the expansion with respect to the inverse of the mass of the nucleon. Close examinations of its properties show that it can be expressed with good accuracy by a local potential in x-space at low energies (below nearly 300 Mev). Nonstatic parts of the potential have different signs accordings as whether the assumed coupling between the pion and the nucleon is pseudoscalar or pseudovector. Comparison with the experimental phase shifts is briefly discussed. It is shown in the case of the pseudoscalar coupling that the nonstatic one-pion-exchange potential derived in this paper is almost exact from the theoretical point of view when the distance between two nucleons is far enough (large compared with one third of the pion Compton wavelength). It is also argued on some physical assumptions that the potential will in fact be exact in the case of the pseudovector coupling too.