This work focuses on the Total Weighted Tardiness Job-Shop Schedul-ing Problem. In this problem, each job consists of a set of tasks that must be processed on a given set of machines for uninterrupted and predetermined time. Each job has a due date and a penalty associated with the delay in comple-tion time. The objective is to minimize the total weighted tardiness. We propose an heuristic method based on Iterated Local Search (ILS) metaheuristic, desig-nated as TWTJSSP-ILS. The method applies GRASP to obtain an initial solution, combining a random choice technique with the longest processing time. In the refinement stage of the ILS method, a Variable Neighborhood Descent (VND) procedure is applied as the as local search step. We present a computational experiment applying this method to the benchmark instances taken from the liter-ature. The initial results lead to high quality solutions.