We propose a new approach for Kronecker compressive sensing of hyperspectral (HS) images, including the imaging mechanism and the corresponding reconstruction method. The proposed mechanism is able to compress the data of all dimensions when sampling, which can be achieved by three fully independent sampling devices. As a result, the mechanism greatly reduces the control points and memory requirement. In addition, we can also select the suitable sparsifying bases and generate the corresponding optimized sensing matrices or change the distribution of sampling ratio for each dimension independently according to different HS images. As the cooperation of the mechanism, we combine the sparsity model and low multilinear-rank model to develop a reconstruction method. Analysis shows that our reconstruction method has a lower computational complexity than the traditional methods based on sparsity model. Simulations verify that the HS images can be reconstructed successfully with very few measurements. In summary, the proposed approach can reduce the complexity and improve the practicability for HS image compressive sensing.