For single-cell multi-user massive multi-input-multi-output (MIMO) system downlink, we consider the per-antenna power constraint and propose a modified maximum-ratio-transmission (MRT) precoding scheme. The outage probability performance of the scheme are analyzed. To enable the analysis, we study the random behaviour of the signal-to-interference-plus-noise-ratio (SINR) and derive an approximation for the probability density function (pdf) of the interference power. Simulation results are shown to validate the theoretical derivations. Moreover, our work show that the massive MIMO system with per-antenna power constraint under the modified MRT precoding can achieve lower outage probability than that with a total power constraint under the standard MRT precoding, even though its power constraint is more strict.