If an e-mail is sent to a user of a communication terminal while the communication terminal is being used for voice communication, informing the user that the e-mail has been sent is controlled. Mobile phone 500 stores an importance level in association with a telephone number and e-mail address. If a mail alert is received while mobile phone 500 is used for voice communication, an importance level of the voice communication partner and an importance level of the sender of the e-mail are read from a nonvolatile memory. The read importance levels are compared by mobile phone 500, and if the importance level of the sender of the e-mail is higher, mobile phone 500 informs the user thereof that it has received the mail alert.