This paper presents one modern heuristic optimisation algorithm, named Taguchi-Based Immune Algorithm (TBIA), to solve the problem of designing 2D recursive digital filters with specified magnitude and group-delay characteristics. The algorithm is detailed for the design of three recursive filters’ categories, namely filters with predefined magnitude, delay and magnitude and delay. On the basis of minimising the magnitude and group-delay errors, multi-criterion design combination is employed to obtain optimal recursive filters that satisfy the required specifications. Computational experiments show the ability of the proposed algorithm to obtain more robust stable complex filters compared with previously reported design methods.