The fifth-generation communications system (5G) will commercialize at 2020 in order to satisfy the increasing demands on data rate and also to enable the internet of things (IoT). One of the most challenging issues in 5G communications network is to provide provisioning quality of service (QoS) while maintaining seamless mobility for user equipment (UE). This paper proposes a QoS-aware handover algorithm based on fuzzy-TOPSIS to trigger and achieve the optimal cell selection. The proposed algorithm integrates both advantages of fuzzy logic and technique for order preference by similarity to an ideal solution (TOPSIS). The weights value of network attributes is first calculated by Entropy and the fuzzy-TOPSIS algorithm are then applied to rank each access networks. This QoS-aware algorithm is able to achieve the optimal Mean Option Score (MOS) for UE by considering QoS related parameters such as network jitter and packet loss ratio. The simulation results indicate that the proposed algorithm can guarantee good QoS while maintaining number of handover at a low level.