Compressed sensing significantly accelerates dynamic magnetic resonance imaging (MRI) by allowing the exact reconstruction of images from a small number of measurements in (k, t)-space. The similarity in three different directions of dynamic MRI makes it have a multi-directional low-rank prior. In this paper, we propose a tensor-based multi-dimensional low-rank regularization for dynamic MRI reconstruction model, termed as MDLRT, and introduce the Schatten capped p-norm to enforce the low-rank prior of multi-directional slices. We take dynamic MRI tensor as processing unit to protect its multi-channel structure and avoid losing internal information, which promises the reconstruction performance. The utilization of multi-directional low-rank characteristics adequately exploits the spatial and temporal redundancies. In addition, using Schatten capped p-norm to regularize the low-rank property realizes a better approximation to the rank than widely used surrogate functions. The proposed model is efficiently solved by the alternating direction multiplier method (ADMM), in which the fast algorithm for each sub-problem is separately developed. In comparison with state-of-the-art methods, extensive experiments on dynamic MR data demonstrate the superior performance and robustness to noise of the proposed method in terms of reconstruction accuracy.