Next generation mobile systems are expected to provide simultaneous multi-service (e.g., voice, data, and streaming) in heterogeneous networks (HNs). In future cellular network environment, network selection algorithm (N.S.A) is important to get the more satisfaction by selecting the best network to consider a lot of QoS parameters such as bandwidth, delay, jitter, and other parameters as stated. Satisfaction degree of users is affected by interruption time of a new call or ongoing call for network setup procedure in this environment. In this paper, we propose a network selection function and a handoff execution algorithm for improving seamless service and throughput. The network selection function considers interruption time of each service, and the handoff execution algorithm reflects QoS satisfaction and seamlessness of totally arising multi-service. Simulation results show that the proposed algorithm supports high throughput and short interruption time for simultaneous multi-service in HN.