This paper proposes an adaptive clonal selection algorithm (CSA) to solve the unrelated parallel machine scheduling problem (UPMSP) with sequence-dependent setup time constraints. The objective is to find the sequence which minimizes the makesepan. CSA is a newly discovered population-based evolutionary algorithm based on the clonal selection principle and the immune system. In order to improve the performance of CSA, a local search operation is adopted to strengthen the search ability. In addition, an adaptive clonal factor and a stage mutation operation are introduced to enhance the exploration and exploitation of the algorithm. The performance of the proposed adaptive clonal selection algorithm is compared with genetic algorithm (GA), Simulated Annealing (SA) and basic CSA on 320 randomly generated instances. The results demonstrate the superiority of the proposed method and confirm its potential to solve the UPMSP with sequence-dependent setup time constraints especially when the scale of the instances is very large.