Objective. Brain–computer interfaces (BCIs) enable a direct communication pathway between the human brain and external devices, without relying on the traditional peripheral nervous and musculoskeletal systems. Motor imagery (MI)-based BCIs have attracted significant interest for their potential in motor rehabilitation. However, current algorithms fail to account for the cross-session variability of electroencephalography signals, limiting their practical application. Approach. We proposed a Riemannian geometry-based adaptive boosting and voting ensemble (RAVE) algorithm to address this issue. Our approach segmented the MI period into multiple sub-datasets using a sliding window approach and extracted features from each sub-dataset using Riemannian geometry. We then trained adaptive boosting (AdaBoost) ensemble learning classifiers for each sub-dataset, with the final BCI output determined by majority voting of all classifiers. We tested our proposed RAVE algorithm and eight other competing algorithms on four datasets (Pan2023, BNCI001-2014, BNCI001-2015, BNCI004-2015). Main results. Our results showed that, in the cross-session scenario, the RAVE algorithm outperformed the eight other competing algorithms significantly under different within-session training sample sizes. Compared to traditional algorithms that involved a large number of training samples, the RAVE algorithm achieved similar or even better classification performance on the datasets (Pan2023, BNCI001-2014, BNCI001-2015), even when it did not use or only used a small number of within-session training samples. Significance. These findings indicate that our cross-session decoding strategy could enable MI-BCI applications that require no or minimal training process.