A mail server with a forwarding function provided for a company mail server or an ISP mail server with which a user belonging to the company is contracted has at least a user table storing user passwords and the like; an address table storing forwarding addresses for each user; regulating tables for regulating the forwarding time periods of each day and the number of characters in a forwarded e-mail for each forwarding address; and a rejection table for preventing some e-mail from being forwarded based on the contents of the e-mail header or the text. Provided a user is authenticated by a password, the user can assign daily forwarding time periods stored in the table for each of a plurality of terminals, such as a home computer, cellular telephone, or other portable terminal. The user can also input weekly conditions for canceling such forwarding. When the mail server receives e-mail, the server references the rejection table to determine whether the incoming e-mail falls within the forwarding conditions. If the e-mail does fall within the forwarding conditions, the server compares the forwarding time period for the destination terminals with the current time and transfers the e-mail to those terminals that conform to the time condition.