For the past 3 years we have been monitoring a sample of 62 K giant stars using precise stellar radial velocity measurements with high accuracy taken at the Thüringer Landessternwarte Tautenburg. We search for sub-stellar companions to giant stars and try to understand the nature of the diverse radial velocity variations exhibited by K giant stars. We present precise stellar radial velocity measurements of the K1III giant star 4 UMa (HD 73108). These were obtained using the coudé echelle spectrograph of 2-m Alfred Jensch Telescope. The wavelength reference for the radial velocity measurements was provided by an iodine absorption cell. Our measurements reveal that the radial velocity of 4 UMa exhibits a periodic variation of 269.3 days with a semiamplitude K = 216.8 m s-1. A Keplerian orbit with an eccentricity, e = 0.43 ± 0.02 is the most reasonable explanation for the radial velocity variations. The orbit yields a mass function, f(m) = (2.05 ± 0.24) × 10- 7~M&sun;. From our high resolution spectra we calculate a metallicity of -0.25 ± 0.05 and derive a stellar mass of 1.23 M&sun; ± 0.15 for the host star. The K giant star 4 UMa hosts a substellar companion with minimum mass M sin i = 7.1 ± 1.6 ~M_Jupiter. Based on observations obtained at the 2-m-Alfred Jensch Telescope at the Thüringer Landessternwarte Tautenburg.