To detect exoplanets and study pulsation of K giant stars, we have observed precise RV (radial velocity) of about 55 early K giant (K0 - K4) stars brighter than V = 5 magnitude since 2003 by using BOES, a high resolution Echelle spectrograph attached to the 1.8 m telescope at BOAO (Bohyunsan Optical Astronomy Observatory). We detected periodic RV variation of KO III star $eta$ Gem (HD 62509) with a period $P;=;596.6;{pm};2.3$ days and a semi-amplitude $K;=;44.8;{pm};0.7;ms^{-1}$. If we adopt 1.7 $M_{odot}$ for the mass of $eta$ Gem, this yields the minimum mass of the companion m sin i = 2.64 $M_{Jupiter}$. Our results agree well with Hatzes et al. (2006) and Reffert et al. (2006), and confirm their discovery of a planetary object around $eta$ Gem. We also confirmed about 192 minutes short period stellar oscillation found by Hatzes and Zechmeister (2007). This is the first report of exoplanet detection using BOES and demonstrates that the RV observation using BOES is accurate and stable enough to detect exoplanets around bright K giant stars.