Accurate and reliable wind direction prediction is important not only for enhancing the efficiency of wind power conversion and ensuring safe operation, but also for promoting sustainable development. Wind direction forecasting is a challenging task due to the random, intermittent and unstable nature of wind direction. This paper proposes a short-term wind direction prediction model based on quadratic decomposition and long short-term memory (LSTM) to improve the accuracy and efficiency of wind direction prediction. Firstly, the model adopts a seasonal-trend decomposition procedure based on the loess (STL) method to divide the wind direction series into three subsequences: trend, seasonality and the remainder, which reduces the impact of the original sequence’s complexity and non-stationarity on the prediction performance. Then, the remainder subsequence is decomposed by the optimal variational mode decomposition (OVMD) method to further explore the potential characteristics of the wind direction sequence. Next, all the subsequences are separately input into the LSTM model, and the prediction results of each subsequence from the model are superimposed to obtain the predicted value. The practical wind direction data from a wind farm were used to evaluate the model. The experimental results indicate that the proposed model has superior performance in the accuracy and stability of wind direction prediction, which also provides support for the efficient operation of wind turbines. By developing advanced wind prediction technologies and methods, we can not only enhance the efficiency of wind power conversion, but also ensure a sustainable and reliable supply of renewable energy.