To search for and study the nature of the long-periodic variations of massive stars, we have been carrying out a precise radial velocity (RV) survey for supergiants. Here, we present high-resolution RV measurements of ${alpha}$ Per which lies near the Cepheid instability strip from November 2005 to February 2011 using the fiber-fed Bohyunsan Observatory Echelle Spectrograph (BOES) at Bohyunsan Optical Astronomy Observatory (BOAO). The orbital solution yields a period of 129 days, a 2K amplitude of 80 m/s, and an eccentricity of 0.1. Assuming a possible stellar mass of 7.3 $M{igodot}$, we estimate the minimum mass for the planetary companion to be 7.5 MJup with the orbital semi-major axis of 0.97 AU. We do not find the correlation between RV variations and chromospheric activity indicator (Ca II H & K region). The Hipparcos photometry and bisector velocity span (BVS) do not show any obvious correlations with RV variations. These analyses suggest that ${alpha}$ Per is a pulsating supergiant that hosts an exoplanet. If the 129 days variations of ${alpha}$ Per do not come from an exoplanet but Cepheid-like pulsations, the theoretical boundary of the Cepheid instability strip may need to be extended to the bluer side.