Magnetic susceptibility and X-band electron spin resonance study of a two-dimensional Heisenberg antiferromagnetic system CuBr2(bipy), where bipy = C10H8N2 is 4,4-bipyridyl, has been performed in the temperature range from 300 K down to 2 K. A rhombic anisotropy of the g-factor was obtained from X-band EPR measurements with gx = 2.037, gy = 2.100 and gz = 2.219. The temperature dependence of the magnetic susceptibility with a round maximum observed at 28 K suggests antiferromagnetic type of short-range order. No signature of the magnetic long-range order in studied compound was observed. The comparison of the magnetic susceptibility data with a two-dimensional rectangular Heisenberg model yields the values of intralayer exchange couplings J/kB = −47 K and J /kB = −9.4 K.