Multi-hop networks have been proposed to increase the data transmission rate in wireless mobile networks, and consequently improve the quality of experience of cell-edge users. A successive resource allocation scheme (SAS) has been proposed for a 2-hop virtual cellular network (VCN). In a multi-cell environment, the performance of SAS degrades because of intra-cell and inter-cell interference. In order to alleviate the effect of intra-cell and inter-cell interference and consequently increase the channel capacity of the VCN, this paper proposes the sequential iterative allocation scheme (SIS). Computer simulation results show that, compared to SAS, SIS can improve the fairness, the ergodic, and the outage channel capacity per mobile terminal (MT) of the VCN in a multi-cell environment. This paper also analyzes the performance of the VCN compared to that of the single hop network (SHN) when SIS is applied in a multi-cell environment. Using SIS, VCN can provide higher ergodic channel capacity, and better degree of fairness than SHN in a multi-cell environment. The effect of the number of wireless ports (WPs) in the VCN is also investigated, and the results suggest that adding more WPs per virtual cell in the VCN can enhance the outage channel capacity per MT and the degree of fairness of the VCN.