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Analyzing electroencephalography (EEG) signals with machine learning approaches has become an attractive research domain for linking the brain to the outside world to establish communication in the name of the Brain-Computer Interface (BCI). Many researchers have been working on developing successful motor imagery (MI)-based BCI systems. However, they still face challenges in producing better performance with them because of the irrelevant features and high computational complexity. Selecting discriminative and relevant features to overcome the existing issues is crucial. In our proposed work, different feature selection algorithms have been studied to reduce the dimension of multiband feature space to improve MI task classification performance. In the procedure, we first decomposed the MI-based EEG signal into four sets of the narrowband signal. Then a common spatial pattern (CSP) approach was employed for each narrowband to extract and combine effective features, producing a high-dimensional feature vector. Three feature selection approaches, named correlation-based feature selection (CFS), minimum redundancy and maximum relevance (mRMR), and multi-subspace randomization and collaboration-based unsupervised feature selection (SRCFS), were used in this study to select the relevant and effective features for improving classification accuracy. Among them, the SRCFS feature selection approach demonstrated outstanding performance for MI classification compared to other schemes. The SRCFS is based on the multiple k-nearest neighbour graphs method for learning feature weight based on the Laplacian score and then discarding the irrelevant features based on the weight value, reducing the feature dimension. Finally, the selected features are fed into the support vector machines (SVM), linear discriminative analysis (LDA), and multi-layer perceptron (MLP) for classification. The proposed model is evaluated with two benchmark datasets, namely BCI Competition III dataset IVA and dataset IIIB, which are publicly available and mainly used to recognize the MI tasks. The LDA classifier with the SRCFS feature selection algorithm exhibits better performance. It proves the superiority of our proposed study compared to the other state-of-the-art BCI-based MI task classification systems.