Carrier aggregation (CA) is proposed to adress the tremendous demands for high data rates in resource limited heterogeneous networks (HetNets). Although the resource allocation problem for CA HetNets has been extensively studied in the literature before, there are still many open challenges, including security threats. Thus, in this paper, a trust-based stable matching (SM) approach is proposed as a solution for selfish user threats in a CA HetNet. The proposed approach aims to provide secure communication to honest users by using a trust index for each user to identify and punish the selfish users gradually. The selfish user identification process in the proposed approach is based on a comparison between the difference of the promised rate and the obtained rate with a predefined threshold after each stable matching round. The identification threshold has a significant role in terms of avoiding false detection of honest users as selfish users as a result of bad channel estimation performances. Additionally, determining an appropriate punishment factor is another essential issue in order to achieve high rate and fairness performances. Thus, appropriate values of the threshold and the punishment factor are investigated in order to achieve a high fairness and low misleading ratio in this study.