In massive MIMO systems, the matched filter (MF) beamformer is an attractive technique due to its extremely low complexity compared with the high-complexity decomposition-based beamforming techniques， such as zero forcing and minimum mean square error. An approximate formula is derived for probability density function (PDF) of the signal-to-interference-and-noise ratio (SINR) at user terminal when multiple antennas and the MF beamformer are used at the base station. The formula is important in calculating or analyzing system performance such as sum-rate and outage probability. Simulations exhibit that the difference between the derived approximate formula for PDF and the simulated PDF approaches zero while the number of antennas at the base station tends to large-scale.