Abstract. This chapter focuses on the construction of chaos-based hash function. Hash function is a special kind of one-way function which takes a variable-length input and returns a fixed-length value. As one of the cores of Cryptography, hashing is a basic technique widely used in information security. Utilizing chaos to construct hash function is a promising direction which attracts more and more attention. In this chapter, some preliminaries on hash function are firstly given in brief. Then, the systemic descriptions of different chaos-based construction approaches are presented in the order of the simple chaotic map-based hash function, the complex map-based hash function, the composite map-based hash function, the chaotic neural network-based hash function, the parallel hash function as well as the combined chaotic cryptographic and hashing scheme. Meanwhile, the detailed analyses of some typical chaos-based hash functions are described. Finally, by borrowing some principles from classical Cryptography, we summarize some instructions on chaos-based hash function secure construction which is beneficial to the hash function design based on chaos in the future.