Abstract.A quaternion model of artificial immune response (AIR) is proposed in this paper. The model abstracts four elements to simulate the process of immune response, namely, antigen, antibody, rules of interaction among antibodies, and the drive algorithm describing how the rules are applied to antibodies. Inspired by the biologic immune system, we design the set of rules as three subsets, namely, the set of clonal selection rules, the set of immunological memory rules, and the set of immunoregulation rules. An example of the drive algorithm is given and a sufficient condition of its convergence is deduced.