Developing accurate wind speed forecasting methods is indispensable to integrating wind energy into smart grids. However, current state-of-the-art wind speed forecasting methods are almost data-driven deep learning models, which may incur potential adversarial cyberattacks. To this end, this paper proposes an adversarial false data injection attack tactic to investigate such a cyber threat. First, targeting the deep learning-based short-term wind speed forecasting model, an optimization model is constructed to obtain the optimally false data that should be injected into the forecasting model input so as to expand the prediction deviation as much as possible. Then, as the optimization model is non-differentiable, a particle swarm optimization-based method is developed to solve the optimization problem, in which the near-optimal solution is able to be explored, directing the false data that should be injected. At last, numerical studies of the proposed attack tactic are conducted on different-hour ahead wind speed forecasting models, revealing the feasibility and effectiveness.