Long Term Evolution-Advanced (LTE-A) networks exploit the Carrier Aggregation (CA) technique to achieve a higher data rate by allowing user equipments (UEs) to simultaneously aggregate multiple component carriers (CCs). Moreover, MIMO technologies have become increasingly mature and been adopted as a default choice of the 4G standards. However, most of existing studies on resource allocation with carrier aggregation do not consider the MIMO capability of UEs. In this paper, we address the spectrum resource allocation problem with consideration of UEs' MIMO capability as well as modulation and coding schemes (MCSs) selection in carrier aggregation based LTE-A systems. We formulate the problem under both backlogged and finite queue traffic models as an optimization model, and prove its NP-hardness. As a result, a 1/2-approximation algorithm is proposed to find a suboptimal solution of resource allocation. Simulation results show that the proposed algorithm outperforms the existing schemes, and performs fairly close to the optimal solution under the small-scale scenarios.