Heterogeneous networks (HetNets) give users the opportunity to access different access points(APs), which will simultaneously affect user performance and system performance, so user association in HetNets plays a critical role in enhancing the load balancing and the system sum-throughput of networks. Meanwhile, the incremental sum-throughput currently fails to meet the escalating data demands. Besides, ensuring fairness amongst users constitutes another urgent issue in the radio resource management (RRM) of HetNets. What is more, few works consider the maximum service user number constraint in femtocell access points (FAPs). To solve the aforementioned problem, this paper associates users to APs by considering system sum-throughput and fairness at the same time in HetNets under a maximum service user number constraint of FAPs; accordingly, the user association problem is formulated. By releasing constraint, the optimal user association algorithm is obtained by Lagrangian function, and based on this optimal solution, a low complexity suboptimal user association algorithm is proposed. At last, this paper investigates the relationship between system sum-throughput and maximum service user number of FAPs. Numerical simulation results show that the proposed algorithm can improve sum-throughput and fairness at the same time at a specific maximum service user number of FAPs.