This paper treats the analytical explicit solution of the moments of the system of the truncated service time Erlangian overflow queue: (M/Er/1/K,M/M/∞) with balking (i.e. the primary queue with limited capacity). The researchers give an explicit solution for M(1), M(2) and M(l). Finally we deduce some particular cases for the two systems: (M/M/1/K,M/M/∞) and (M/E2/1/K,M/M/∞).