This research studies the minimization of the total weighted tardiness in the job shop scheduling problem (JSSP). This problem is NP – strongly Hard and to solve it constructively an implementation of the metaheuristic Ant Colony is proposed. The generated solution is based on the principal of optimal solution that is found in the set of active schedules. The values of different parameters were determined by experimental design. The performance of the proposed heuristic was compared with priority rules and meta-heuristics such as Tabu Search and Simulating Annealing in the solution of instances 5×5, 6×6 y 10×10 that had their optimal solution reported in the literature.