Dictionary learning has drawn increasing attention for its impressive performance in obtaining the high-fidelity representations of data and extracting semantics. However, when there exists distribution divergence between source and target data, the representations of target data based on the learned dictionary from source data fail to reveal the intrinsic nature of target tasks, which consequently degrades the target performance severely. To tackle this problem, we propose a Shared Dictionary Learning (SDL) method in this paper. SDL learns a shared dictionary by implementing both geometric and statistical adaptations. SDL utilizes the Nyström method to exploit the geometric relationships between domains. Specifically, SDL uses the Nyström method to construct a variable source graph based on the target graph eigensystem and employs the Nyström approximation error to measure the distance between the variable source graph and the ground truth source graph to formalize the geometric divergence. Thus, a domain-invariant graph can be constructed by minimizing the approximation error and can be used to bridge two domains geometrically. Simultaneously, SDL captures the latent statistical commonality underlying two domains via minimizing the Maximum Mean Discrepancy (MMD) distance between domains. Finally, SDL achieves a shared dictionary and a set of corresponding new representations to handle cross-distribution data classification. Extensive experimental results on several popular datasets demonstrate the superiority of SDL.