We analyzed Suzaku/XIS data (2006-2015) and Fermi/LAT data (2008-2015) of the gamma-ray emitting radio galaxy NGC 1275. Correlated brightening of the nucleus in both the X-ray and GeV gamma-ray energy bands was found for the period 2013-2015. This is the first evidence of correlated variability between these two energy bands for NGC 1275. We also analyzed Swift/XRT data and found that the X-ray flux increased over several days in 2010, coincidentally with the GeV gamma-ray flare. During the flare, the X-ray spectra were softer, with a photon index of ∼2 compared with 1.5-2.1 of the other periods, suggesting the brightening of a synchrotron component. The GeV gamma-ray band also showed a higher flux with a harder spectrum during the 2010 flare. Simultaneous X-ray and GeV gamma-ray flux increase in the flare could be explained by the shock-in-jet scenario. On the other hand, a long-term gradual brightening of radio, X-ray, and GeV gamma-ray flux with a larger gamma-ray amplitude could have an origin other than internal shocks, and some of these possibilities are discussed.