In this paper, an asymptotic distribution for the sum rate capacity is derived in zero-forcing beamforming (ZF-BF) based multiuser MIMO systems with a large number of base station (BS) antennas. By utilizing the characteristics of a large number of antennas and the central limit theorem, we prove that the asymptotic distribution for the sum rate capacity follows Gaussian distribution. Also we derive the mean and variance values for the asymptotic Gaussian distribution. Based on the asymptotic Gaussian distribution, we also obtain the outage probability for the sum rate capacity as a closed form. Simulation results show that the asymptotic Gaussian distribution is well follows the actual sum rate capacity, and the both asymptotic mean and variance value are also very accurate.