This paper presents a novel motor imagery classification algorithm that uses an overlapping multiscale multiband convolutional Riemannian network with band-wise Riemannian triplet loss to improve classification performance. Despite the superior performance of the Riemannian approach over the common spatial pattern filter approach, deep learning methods that generalize the Riemannian approach have received less attention. The proposed algorithm develops a state-of-the-art multiband Riemannian network that reduces the potential overfitting problem of Riemannian networks, a drawback of Riemannian networks due to their inherent large feature dimension from covariance matrix, by using fewer subbands with discriminative frequency diversity, by inserting convolutional layers before computing the subband covariance matrix, and by regularizing subband networks with Riemannian triplet loss. The proposed method is evaluated using the publicly available datasets, the BCI Competition IV dataset 2a and the OpenBMI dataset. The experimental results confirm that the proposed method improves performance, in particular achieving state-of-the-art classification accuracy among the currently studied Riemannian networks.