An apparatus and a method for configuring security for connection between a portable terminal supporting a Wireless-Fidelity (Wi-Fi) function and an Access Point (AP) are provided. More particularly, an apparatus and a method are provided for preventing access failure caused by an access request of a portable terminal while an AP of an un-configured mode, which is completing security setup using a Wi-Fi Protected Setup (WPS) function, is rebooted. The apparatus includes an AP for providing a terminal with a time taken to reboot after configuring security information based on a WPS function in an un-configured mode, wherein the terminal sends a request to access the AP after the rebooting has completed by determining the time taken to reboot received from the AP of the un-configured mode.