An algorithm for one-way Hash function construction based on tangent-delay ellipse reflecting cavity-map system (TD-ERCS) is proposed in this paper. In the algorithm, the plaintext dealt with is first transformed into a systemic parameter sequence linearly, and then TD-ERCS is iterated in order of the parameter sequence directly, the final Hash value of 160 bits is obtained by means of the nonlinear transform on the iteration sequence, and no padding of calculation is added. Users’ keys of the algorithm can be chosen in the region［264, 2160］ arbitrarily. Theoretical analysis and basic security tests indicate that our Hash function has good one-way, weak collision property, better security than other chaotic Hash functions, and it can be realized easily with great rapidity. Our algorithm of Hash function is an ideal substitution for conventional Hash function. And also, a natural criterion (theoretical value of 85.33) to evaluate collision property of Hash function is educed in this paper.