A variety of multi-carrier schemes called new-waveforms have been studied in order to make up for the weak points of cyclic prefix - orthogonal frequency division multiplexing (CP-OFDM). Due to its spectral efficiency and well-localized spectrum, a quadrature amplitude modulation based filter-bank multi-carrier (QAM-FBMC) is considered as one of the candidate for 5G mobile communications. In this paper, we describe the criterion for the well-designed filter and suggest the new one whose filter coefficients are composed of real number only. Simulation results show that the QAM-FBMC systems are superior to the spectral efficiency compared to CP-OFDM. Moreover, a new designed filter shows the improvement of the performance in comparison with the conventional QAM-FBMC systems.