This work investigates a dynamic constrained multi-objective optimization immune algorithm solving a class of extremely difficult multi-objective optimization problems with constraints and time-variant dimensions of decision space. In designs of the algorithm, several adaptive immune operators relying upon the metaphors of antibody learning are designed to evolve the current antibody population, while an environmental recognition rule, in terms of the function of antibody recognition, is developed to step up the process of optimization for similar or identical environments. On the other hand, the concept of non-dominance is used to design an antibody evaluation scheme, while the environmental memory set and memory pool as well as the rule of antibody selection are constructed based on the functions of memory and dynamic balance maintenance respectively. Depending on three performance indexes proposed and two popular algorithms compared, numerical experiments show that the proposed algorithm has satisfactory searching effect and the ability of strong environmental tracking.