Objective. Due to low spatial resolution and poor signal-to-noise ratio of electroencephalogram (EEG), high accuracy classifications still suffer from lots of obstacles in the context of motor imagery (MI)-based brain-machine interface (BMI) systems. Particularly, it is extremely challenging to decode multiclass MI EEG from the same upper limb. This research proposes a novel feature learning approach to address the classification problem of 6-class MI tasks, including imaginary elbow flexion/extension, wrist supination/pronation, and hand close/open within the unilateral upper limb.Approach. Instead of the traditional common spatial pattern (CSP) or filter-bank CSP (FBCSP) manner, the Riemannian geometry (RG) framework involving Riemannian distance and Riemannian mean was directly adopted to extract tangent space (TS) features from spatial covariance matrices of the MI EEG trials. Subsequently, to reduce the dimensionality of the TS features, the algorithm of partial least squares regression was applied to obtain more separable and compact feature representations.Main results. The performance of the learned RG feature representations was validated by a linear discriminative analysis and support vector machine classifier, with an average accuracy of 80.50% and 79.70% on EEG dataset collected from 12 participants, respectively.Significance. These results demonstrate that compared with CSP and FBCSP features, the proposed approach can significantly increase the decoding accuracy for multiclass MI tasks from the same upper limb. This approach is promising and could potentially be applied in the context of MI-based BMI control of a robotic arm or a neural prosthesis for motor disabled patients with highly impaired upper limb.