This paper proposes a generalized frequency division multiplexing (GFDM) modulation scheme that transmits a signal with different subcarrier bandwidths. In a receiver, the GFDM signal is demodulated by using a zero forcing (ZF) algorithm or a minimum mean square error (MMSE) algorithm and the BER performance of these algorithms is related to the condition number of a modulation matrix. This matrix can be optimized by adjusting the roll-off factor of subcarrier filters. It is shown that the performance of the proposed GFDM is about 0.02 dB better than that with a roll-off factor of 0 at a BER of 10-3 on an AWGN channel. On the other hand, on the multipath fading channels, the BER performance improves as the subcarrier bandwidth increases because of frequency diversity.