Classification accuracy achieved by a machine learning technique depends on the feature set used in the learning process. However, it is often found that all the features extracted by some means for a particular task do not contribute to the classification process. Feature selection (FS) is an imperative and challenging pre-processing technique that helps to discard the unnecessary and irrelevant features while reducing the computational time and space requirement and increasing the classification accuracy. Generalized Normal Distribution Optimizer (GNDO), a recently proposed meta-heuristic algorithm, can be used to solve any optimization problem. In this paper, a hybrid version of GNDO with Simulated Annealing (SA) called Binary Simulated Normal Distribution Optimizer (BSNDO) is proposed which uses SA as a local search to achieve higher classification accuracy. The proposed method is evaluated on 18 well-known UCI datasets and compared with its predecessor as well as some popular FS methods. Moreover, this method is tested on high dimensional microarray datasets to prove its worth in real-life datasets. On top of that, it is also applied to a COVID-19 dataset for classification purposes. The obtained results prove the usefulness of BSNDO as a FS method. The source code of this work is publicly available at https://github.com/ahmed-shameem/Feature_selection.