Because of the scarcity of spectrum and energy resource, the problems about allocation of these resources become more and more important in recent years. However, inappropriate resource allocation may bring about high inter-cell interference which has a great effect on the performance of the entire system. Thus, in this paper, considering inter-cell interference, we provide the optimal formulation of the resource allocation problem and divide it into two sub-problems, including the component carrier (CC) selection problem and the power allocation problem. The proposed enhanced data rate component carrier selection (EDR-CCS) scheme not only reduces the inter-cell interference but also maximizes the UEs' data transmission rates. Regarding the power allocation problem, two schemes (i.e., geometry programming power allocation (GPPA) and constant interference power allocation (CIPA)) are proposed with the target of finding suboptimal solutions to the power allocation problem under the constraints of eNB's maximum transmission power and UEs' transmission rate requirement on the control channel of primary CC (PCC). Simulation results demonstrate that the data rate performance of EDR-CCS scheme is better than that of random CC selection scheme. Furthermore, GPPA scheme can achieve better performance than CIPA scheme since the GPPA scheme can accommodate the variations from inter-cell interference.