Radio link failures and service interruption times in a multi-connectivity session can be reduced or ideally avoided by means of simultaneous connections of multiple base stations (BSs). This advantage of multi-connectivity has encouraged researchers to embed multi-connectivity technology in several network scenarios. For example, the use of multi- connectivity in 5G ultra-dense networks (UDNs) effectively improves spectrum utilization and average user throughput. In this context, resource allocation has to be carefully considered in UDNs. Therefore, this paper proposes an improved proportional fair resource-scheduling scheme, where the user first dynamically selects the cooperative BSs according to the reference signal received power (RSRP) and then determines the priority of the user based on load balancing, user characteristics, and fairness. Simulation results show that the proposed scheme notably improves the system throughput.