In this paper a two-agent flow shop scheduling problem is studied and a simple parallel iterated local search algorithm is proposed to minimize the makespan of jobs from the first agent and the total tardiness of jobs from the second agent simultaneously. Parallelization is implemented by applying multiple independent searches, each of which uses three neighborhood structures with dynamical transition mechanism. The current solution of each independent search is replaced with a solution, which is randomly chosen from the non-dominated set and perturbed. The computational experiments show the promising advantage of the proposed method when compared to other algorithms of the problem.