In motor imagery (MI) based brain-computer interface (BCI) signal analysis, mu and beta rhythms of electroencephalograms (EEGs) are widely investigated due to their high temporal resolution and capability to define the different movement-related mental tasks separately. However, due to the high dimensions and subject-specific behaviour of EEG features, there is a need for a suitable feature selection algorithm that can select the optimal features to give the best classification performance along with increased computational efficiency. The present study proposes a feature selection algorithm based on neighbourhood component analysis (NCA) with modification of the regularization parameter. In the experiment, time, frequency, and phase features of the EEG are extracted using a dual-tree complex wavelet transform (DTCWT). Afterwards, the proposed algorithm selects the most significant EEG features, and using these selected features, a support vector machine (SVM) classifier performs the classification of MI signals. The proposed algorithm has been validated experimentally on two public BCI datasets (BCI Competition II Dataset III and BCI Competition IV Dataset 2b). The classification performance of the algorithm is quantified by the average accuracy and kappa coefficient, whose values are 80.7% and 0.615 respectively. The performance of the proposed algorithm is compared with standard feature selection methods based on Genetic Algorithm (GA), Principal Component Analysis (PCA), and ReliefF and performs better than these methods. Further, the proposed algorithm selects the lowest number of features and results in increased computational efficiency, which makes it a promising feature selection tool for an MI-based BCI system.