Abstract: A hash function based on triple-block chaining (HTBC) is put forward and its security is demonstrated. The speed of the HTBC algorithm is faster than that of hash functions in common use (SHA and MD family). The dependence test results accord with the demands. The HTBC algorithm is complete; its degree of avalanche effect is about 0.9993; its degree of strict avalanche criterion is 0.992 or so. The frequency test results indicate that the output generated by the HTBC algorithm has uniformity. The binary matrix rank test results indicate that it is linear independent among disjoint sub-matrices of the output. Maurer's universal statistical test results show that the output could be significantly compressed without loss of information. The results of run test, spectral test, non-overlapping template matching test, overlapping template matching test, Lempel-Ziv compression test, linear complexity test, serial test, approximate entropy test, cumulative sums test, random excursions test, and random excursions variant test all fulfill the requirements. Therefore the output generated by the HTBC algorithm has good pseudo-randomness. Thus the security of the HTBC algorithm is verified by way of statistical evaluation.