Electroencephalogram (EEG) signal classification plays an important role to facilitate physically impaired patients by providing brain-computer interface (BCI)-controlled devices. However, practical applications of BCI make it difficult to decode motor imagery-based brain signals for multiclass classification due to their non-stationary nature. In this study, we aim to improve multiclass classification accuracy for motor imagery movement using sub-band common spatial patterns with sequential feature selection (SBCSP-SBFS) method. Filter bank having bandpass filters of different overlapped frequency cutoffs is applied to suppress the noise signals from raw EEG signals. The output of these sub-band filters is sent for feature extraction by applying common spatial pattern (CSP) and linear discriminant analysis (LDA). As all of the extracted features are not necessary for classification therefore, selection of optimal features is done by passing the extracted features to sequential backward floating selection (SBFS) technique. Three different classifiers were then trained on these optimal features, i.e., support vector machine (SVM), Naïve-Bayesian Parzen-Window (NBPW), and k-Nearest Neighbor (KNN). Results are evaluated on two datasets, i.e., Emotiv Epoc and wet gel electrodes for three classes, i.e., right-hand motor imagery, left hand motor imagery, and rest state. The proposed model yields a maximum accuracy of 60.61% in case of Emotiv Epoc headset and 86.50% for wet gel electrodes. The computed accuracy shows an increase of 7% as compared to previously implemented multiclass EEG classification.