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This paper considers the permutation flowshop scheduling problem with blocking in-process with the objective of minimizing the total tardiness of jobs. In this problem there are no buffers between successive machines, that is, it is not allowed intermediate queues of jobs waiting in the system for their subsequent operations. To solve the problem, we propose a genetic algorithm that includes strategies like local search, a procedure to control over the diversity of the population and a intensification procedure based on the path relinking technique. The path relinking technique generates new solutions transforming one elite solution to another one of the population. The performance of the proposed genetic algorithm is evaluated comparing with a GRASP metaheuristic with path relinking from the literature. Computational tests show that the genetic algorithm is very efficient and promising.