This paper considers the parallel-machine scheduling with preference of machines so as to minimizing total tardiness. An immunoglobulin-based artificial immune (IAI) algorithm is constructed for searching the best production sequence of aluminum foil factory. The IAI algorithm has a systematic immune mechanism which mainly is built on somatic hypermutation and recombination methods. There are three categories of immunoglobulin in somatic hypermutation for constructing antibody proliferation mechanism to obtain superior antibodies. To avoid falling into local optimal solutions, receptor editing mechanism suppresses the worse solutions to accelerate convergence. And reverse mechanism is developed in somatic recombination to generate some new antibodies. The computational results show that the performance of IAI is significant improvement to the EDD based heuristic. Therefore, the proposed IAI algorithm is competitive for the parallel-machine scheduling problem.