High spectral efficiency is considered as one of the most significant requirements that should be achieved in LTE-Advanced standard in order to fulfil the requirements of IMT-Advanced technology. Carrier Aggregation (CA) and Adaptive Modulation and Coding (AMC) techniques are considered as two potential techniques that can provide high spectral efficiency in wireless communication systems. In this paper, CA technique employing AMC scheme will be implemented to further enhance spectral efficiency performance. Meanwhile, this paper is targeted to simplify a mathematical formulation for calculating spectral efficiency when CA technique is implemented employing AMC scheme. Simulation results show that, the CA technique employing AMC scheme based on the formulated mathematical expression significantly achieve the best possible performance in terms of spectral efficiency in the downlink transmission compared to the performance of Non-CA based on single Component Carrier (CC) employing AMC scheme.