Context: For the past 3 years we have been monitoring a sample of 62 K giant stars using precise stellar radial velocity measurements taken at the Thueringer Landessternwarte Tautenburg. Aims: To search for sub-stellar companions to giant stars and to understand the nature of the diverse radial velocity variations exhibited by K giant stars. Methods: We present precise stellar radial velocity measurements of the K1III giant star 4 UMa (HD 73108). These were obtained using the coude echelle spectrograph of 2-m Alfred Jensch Telescope. The wavelength reference for the radial velocity measurements was provided by an iodine absorption cell. Results: 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. 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) x 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. Conclusions: The K giant star 4 UMa hosts a substellar companion with minimum mass m sin i = 7.1 +/- 1.6 M_Jupiter.