As one of the most classical scheduling problems, flexible job shop scheduling problems (FJSP) find widespread applications in modern intelligent manufacturing systems. However, the majority of meta-heuristic methods for solving FJSP in the literature are population-based evolutionary algorithms, which are complex and time-consuming. In this paper, we propose a fast effective single-solution based local search algorithm with an innovative adaptive weighting-based local search (AWLS) technique for solving FJSP. The adaptive weighting technique assigns weights to each operation and adaptively updates them during the exploration. AWLS integrates a Tabu Search strategy and the adaptive weighting technique to smooth the landscape of the search space and enhance the exploration diversity. Computational experiments on 313 well-known benchmark instances demonstrate that AWLS is highly competitive with state-of-the-art algorithms in terms of both solution quality and computational efficiency, despite of its simplicity. Specifically, AWLS improves the previous best-known results in the literature on 33 instances and match the best-known results on the remaining ones except for only one under the same time limit of up to 300 s. As a strongly non-deterministic polynomia (NP)-hard problem which has been extensively studied for nearly half a century, breaking the records on these classic instances is an arduous task. Nevertheless, AWLS establishes new records on 8 challenging instances whose previous best records were established by a state-of-the-art meta-heuristic algorithm and a famous industrial solver.