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The mixture of users with different carrier aggregation (CA) capabilities presents new challenges to optimize the performance of the next generation wireless networks. This paper focuses on the joint resources allocation for OFDMA-based multi-carrier system. Distinguished from many existing methods, our approach deploys the joint dynamic spectrum resources assignment and adaptive power allocation technologies for the carrier-aggregated systems. A low complexity suboptimal algorithm, named as the joint CC, RB and power allocation (JCRPA) algorithm, is proposed in this paper. The algorithm combines the dynamic component carrier (CC) and resource block (RB) assignment, as well as adaptive power allocation iteratively. In contrast to the conventional static CC assignment, a novel suboptimal dynamic CC and RB assignment algorithm is designed to maximize network utility. Simulation results demonstrate that JCRPA is able to improve the system performance in terms of network utility, average throughput and fairness.