This paper presents a novel pre-shared key (PSK) agreement scheme to establish a secure connection between a Wi-Fi client and access point (AP) without prior knowledge of a password. The standard IEEE 802.11 security method, Robust Security Network Association, widely known as Wi-Fi Protected Access (WPA) and WPA2, derives a shared cryptographic key if and only if a user provides an identical password which an AP possesses, causing ofinconvenience of obtaining and entering the password. In this paper, a proposed scheme, Secure Open AP (SOAP), adopts two public key algorithms, the elliptic curve Diffie-Hellman key exchange algorithm (ECDH) and digital signature algorithm (ECDSA) to establish a secure connection between a client and an AP without having prior knowledge of a password. Implementation and experiment results demonstrate the viability of the proposed scheme.