The conventional receiver designs of generalized frequency division multiplexing (GFDM) system assume full subcarrier allocation. In this case, the optimal linear receivers can be implemented with low-complexity channel equalization followed by zero-forcing (ZF) demodulation. In some use cases, e.g. multiuser, only a subset of the subcarriers is active for data transmission. Therefore, the optimal receiver design needs to consider the effective joint channel and modulation matrix, which complicates the practical implementation. To maintain low-complexity realization in these cases, full allocation can still be assumed, however, the performance loss is remarkable. In this paper, we propose an efficient transceiver design for non-fully allocated GFDM system. In the proposed approach, the frequency-domain (FD) sparsity of GFDM is exploited to represent the transmitted signal by means of an effective small-size GFDM model with one non-active subcarrier. Therefore, the assumption of full allocation becomes more realistic. Moreover, the received signal can be further reformulated with fully allocated system, but at the cost of altering the effective channel gains. The proposed design significantly reduces the computation cost of the practical GFDM receiver, whereas the performance still approaches the counterpart optimal linear receiver.