There are various fields are affected by the growth of data dimensionality. The major problems which are resulted from high dimensionality of data including high memory requirements, high computational cost, and low machine learning classifier performance. Therefore, proper selection of relevant features from the set of available features and the removal of irrelevant features will solve these problems. Therefore, to solve the feature selection problem, an improved version of Dragonfly Algorithm (DA) is proposed by combining it with Simulated Annealing (SA), where the improved algorithm named BDA-SA. To solve the local optima problem of DA and enhance its ability in selecting the best subset of features for classification problems, Simulated Annealing (SA) was applied to the best solution found by Binary Dragonfly algorithm in attempt to improve its accuracy. A set of frequently used data sets from UCI repository was utilized to evaluate the performance of the proposed FS approach. Results show that the proposed hybrid approach, named BDA-SA, has superior performance when compared to wrapper-based FS methods including a feature selection method based on the basic version of Binary Dragonfly Algorithm.