A secure and efficient mutual authentication and key agreement scheme is critical to the security of wireless sensor networks (WSNs). Recently, many authentication schemes for multi-gateway WSNs have been proposed, but most of them are then found to have various security problems. By carefully analyzing Guo et al.’s scheme (2019), we point out its security weaknesses with causes. Besides being vulnerable to known attacks, this scheme is also prone to single point of failure. This paper proposes a novel elliptic curve cryptography (ECC) based three-factor authentication scheme for multi-gateway WSNs. The proposed scheme limits password guessing attempts and realizes ideal features like local password change, smart card revocation, dynamic sensor node addition, etc. The user is allowed to register on two frequently visited gateway nodes with the same smart card to withstand single point of failure and reduce cross-gateway communication requirements, which improves the authentication efficiency. BAN-logic and ProVerif tool are used to prove the correctness and security of the mutual authentication and key agreement process. Heuristic analysis shows the proposed scheme can resist various known attacks. Compared with other related schemes for multi-gateway WSNs, the proposed scheme can provide higher level of security efficiently.