The nearby Seyfert type galaxy NGC 1275 contains a bright radio nucleus at its center, revealed through high-spatial resolution imaging to be the source of the jets emanating from the galaxy. Coincident with the emergence of a new component C3 in the nucleus since 2005, flux densities from NGC 1275, at least at radio, millimeter (mm), and γ-ray frequencies, had been increasing up through 2017 and leveled off afterwards. We analyze the long-term light curves of the nucleus that span the rising trend to 2015 July, and find a pair of approximately year-long quasi-periodic oscillations, with periods of P l 345 d and P h 386 d respectively, in emission at 1.3-mm wavelength. We discuss the case that there would be a long precession period P prec 9 yr, causing the appearance of P h that is slightly higher than P l . The accretion disk around the central supermassive black hole (SMBH) would be precessing at P prec , induced by either the Lense-Thirring effect or the existence of a companion SMBH. In the two scenarios, P l would be the jet wobbling timescale or the SMBH binary period respectively. The finding, which could be verified through high-spatial resolution mm imaging, would not only identify the nature of the jet variation but also help reveal the full features of the galaxy.