A filter-bank multicarrier - quadrature amplitude modulation (FBMC-QAM) system with two prototype filters for transmitting QAM signal is proposed. The proposed transmitter performs separate filtering for the even-numbered sub-carrier symbols and the odd-numbered sub-carrier symbols. We derive the orthogonality conditions for a FBMC-QAM system without the intrinsic interference. In order to satisfy the suggested orthogonality conditions, we perform a kind of block interleaving for the odd-numbered sub-carrier filtering. The receiver structure is the counterpart to the transmitter. Numerical results showed that the proposed FBMC-QAM system has almost the same bit error rate (BER) performance compared to the FBMC-OQAM and the orthogonal frequency division multiplexing (OFDM) system. with the proposed FBMC-QAM, multiple-input multiple-output transmission schemes and channel estimation schemes can be utilized similarly as in OFDM.