This paper deals with a bi-objective hybrid no-wait flowshop scheduling problem minimizing the make span and total weighted tardiness, in which we consider transportation times between stages. Obtaining an optimal solution for this type of complex, large-sized problem in a reasonable computational time by using traditional approaches and optimization tools is extremely difficult. This paper, therefore, presents a new multi-objective simulated annealing algorithm (MOSA). A set of experimental instances are carried out to evaluate the algorithm by advanced multi-objective performance measures. In fact, the performance of the algorithm is carefully evaluated in terms of the available algorithms by means of multi-objective performance measures and statistical tools. The results show that compared with other algorithms, a variant of our proposed MOSA produces a good performance.