We report a possible low-mass companion around the K2 III star $varepsilon$ CrB (HD 143107). This star belongs to our sample of 55 K-giants studied for their radial velocity variations using the fiber-fed Bohyunsan Observatory Echelle Spectrograph (BOES) attached to the 1.8-m telescope at Bohyunsan Optical Astronomy Observatory (BOAO). Our precise radial velocity measurements were obtained from February 2005 to June 2010. We find an orbital solution with a period of P = 419 days, a semi-amplitude of K = 137 m/s, and an eccentricity of e = 0.14. Assuming a moderate stellar mass of $M_{igstar}=0.77;Modot$, we calculate the minimum mass for the companion of m sini = $4.2;M_{Jup}$ with an orbital semi-major axis of 1.0 AU.