In this paper, we propose a new quadrature amplitude modulation (QAM) based filter bank multi-carrier (FBMC) system using faster-than-Nyquist (FTN) scheme with block-wise interleaved filters. The proposed QAM-FBMC system can be implemented by block transform processing to have well-localization in time and frequency domains. The proposed QAM-FBMC system does not have time and frequency overheads such as cyclic prefix (CP), tail and guard band. In addition, the FTN scheme is applied to boost the spectral efficiency. Also, the proposed QAM-FBMC system can compensate interference more effectively using maximum likelihood sequence equalization in frequency domain. Simulation results shows the better bit error rate performances at high signal-to-noise ratios than the CP-OFDM systems. Therefore, the proposed QAM-FBMC system can achieve high spectral efficiency by reduction of time and frequency overheads and the FTN signaling.