Aiming at the problem that the computation complexity of the existing minimum mean square error (MMSE) demodulator with generalized frequency division multiplexing (GFDM) over frequency selective channel is relatively high, a matrix deconstruction based low-complexity MMSE GFDM receiver is proposed. By utilization of the particular structures (sparse, quasi-tridiagonal, block-symmetric, etc.) in a series of large-sized matrices involved in the receiver, either of large-sized matrix manipulations (including matrix multiplication and matrix inversion) is partitioned into small-sized matrix manipulations, thereby considerably reducing the computational complexity. Quantitively speaking, the times of complex multiplications consumed by the proposed MMSE receiver is 2-3 amount levels lower than the original MMSE receiver. Moreover, simulation shows that the proposed receiver does not suffer from any bit-error-rate degradation. Therefore, the proposed MMSE GFDM receiver possesses vast potentials for future 5G demodulation applications.