Time-critical-communication, which should guarantee a time limit of a communication service is getting important in multimedia and factory automation fields. This paper proposes an IP-based protocol, Network Protocol with Performance (NPP) to provide the advanced best-effort service which takes a time constraint into account for real-time applications on the Internet. NPP uses the packet-scheduling function to make an effort to guarantee time constraints. Packet-scheduling algorithm chooses a packet in a NPP queue by a precedent level and a time constraint of each packet. We also discuss an application of NPP to multimedia communication system, and investigate performance of NPP by simulation.