In this paper, we focus on one of the representative 5G network scenarios, namely multi-tier heterogeneous cellular networks. User association is investigated in order to reduce the down-link co-channel interference. Firstly, in order to analyze the multi-tier heterogeneous cellular networks where the base stations in different tiers usually adopt different transmission powers, we propose a Transmission Power Normalization Model (TPNM), which is able to convert a multi-tier cellular network into a single-tier network, such that all base stations have the same normalized transmission power. Then using TPNM, the signal and interference received at any point in the complex multi-tier environment can be analyzed by considering the same point in the equivalent single-tier cellular network model, thus significantly simplifying the analysis. On this basis, we propose a new user association scheme in heterogeneous cellular networks, where the base station that leads to the smallest interference to other co-channel mobile stations is chosen from a set of candidate base stations that satisfy the quality-of-service (QoS) constraint for an intended mobile station. Numerical results show that the proposed user association scheme is able to significantly reduce the down-link interference compared with existing schemes while maintaining a reasonably good QoS.