A connection accepting system, an accepting server, and a connection-acceptance managing method, for reducing the processing load of a server and allowing connection to the server in the order of arrival of connection requests. An accepting server accepts a connection request to an application server made from a client terminal through a network. The accepting server issues a reference number to the client terminal at the time of receiving a first connection request, and manages a connection priority for connection to the application server, based on the reference number. The accepting server transmits a program for automatically executing a connection request again after a predetermined time period, at the time of issuing the reference number to the client terminal.