Heterogeneous wireless sensor networks (HEWSN) is a kind of wireless sensor networks (WSN), each sensor may has different attributes, HEWSN has been widely used in many aspects. Due to sensors are deployed in unattended environments and its resource constrained feature, the design of security and efficiency balanced authentication scheme for HEWSN becomes a vital challenge. In this paper, we propose a secure and lightweight user authentication and key agreement scheme based on biometric for HEWSN. Firstly, fuzzy extractor is adopted to handle the user's biometric information. Secondly, we achieve mutual authentication and key agreement among three entities, which are user, gateway and cluster head in the four phases. Finally, formal security analysis shows that the proposed scheme defends against various security pitfalls. Additionally, comparison results with other surviving relevant schemes show that our scheme is more efficient in term of computational cost, communication cost and estimated time. Therefore, the proposed scheme is well suitable for practical application in HEWSN.