The classification of limb movements can provide with control commands in non-invasive brain-computer interface. Previous studies on the classification of limb movements have focused on the classification of left/right limbs; however, the classification of different types of upper limb movements has often been ignored despite that it provides more active-evoked control commands in the brain-computer interface. Nevertheless, few machine learning method can be used as the state-of-the-art method in the multi-class classification of limb movements. This work focuses on the multi-class classification of upper limb movements and proposes the multi-class filter bank task-related component analysis (mFBTRCA) method, which consists of three steps: spatial filtering, similarity measuring and filter bank selection. The spatial filter, namely the task-related component analysis, is first used to remove noise from EEG signals. The canonical correlation measures the similarity of the spatial-filtered signals and is used for feature extraction. The correlation features are extracted from multiple low-frequency filter banks. The minimum-redundancy maximum-relevance selects the essential features from all the correlation features, and finally, the support vector machine is used to classify the selected features. The proposed method compared against previously used models is evaluated using two datasets. mFBTRCA achieved a classification accuracy of 0.4193 ± 0.0780 (7 classes) and 0.4032 ± 0.0714 (5 classes), respectively, which improves on the best accuracies achieved using the compared methods (0.3590 ± 0.0645 and 0.3159 ± 0.0736, respectively). The proposed method is expected to provide more control commands in the applications of non-invasive brain-computer interfaces.