We report the detection of an exoplanet candidate in orbit around σ Persei from a radial velocity (RV) survey. The system exhibits periodic RV variations of 579.8 ± 2.4 days. The purpose of the survey is to search for low-amplitude and long-period RV variations in giants and examine the origin of the variations using the fiber-fed Bohyunsan Observatory Echelle Spectrograph installed at the 1.8- m telescope of Bohyunsan Optical Astronomy Observatory in Korea. We present high-accuracy RV measurements of σ Per made from December 2003 to January 2014. We argue that the RV variations are not related to the surface inhomogeneities but instead a Keplerian motion of the planetary companion is the most likely explanation. Assuming a stellar mass of 2.25 ± 0.5 M⊙, we obtain a minimum planetary companion mass of 6.5 ± 1.0 MJup, with an orbital semi-major axis of 1.8 ± 0.1 AU, and an eccentricity of 0.3 ± 0.1 around σ Per.