Tensor greedy algorithms are widely used in the compressive sensing of multidimensional data such as hyperspectral (HS) images. However, due to their single-atom selection approach, the traditional tensor greedy algorithms sometimes cannot provide a satisfactory speed. We propose an algorithm, containing two modes, to select multiatoms instead of selecting a single atom during each iteration. The first one is an intuitive mode which means to select a fixed number of atoms in each iteration, in order to speed up the reconstruction. As an improvement, we develop the second mode in which the number of selected atoms for each iteration decreases gradually. A larger number of atoms is selected in the former iterations aiming to obtain enough speed while a smaller number in later iterations aims to guarantee the reconstruction accuracy. We have also studied the effect of parameters in the algorithm on reconstruction and determined the proper parameter ranges. The performance of the proposed algorithm is verified by both synthetic data and HS image simulations. Moreover, we compare the proposed algorithm with a traditional tensor greedy algorithm, demonstrating that the reconstruction speed is greatly improved without compromising accuracy.