Hyperpolarized (HP) gas (e.g., 3He or 129Xe) dynamic MRI could visualize the lung ventilation process, which provides characteristics regarding lung physiology and pathophysiology. Compressed sensing (CS) is generally used to increase the temporal resolution of such dynamic MRI. Nevertheless, the acceleration factor of CS is constant, which results in difficulties in precisely observing and/or measuring dynamic ventilation process due to bifurcating network structure of the lung. Here, an adaptive strategy is proposed to highly undersample pulmonary HP dynamic k-space data, according to the characteristics of both lung structure and gas motion. After that, a valid reconstruction algorithm is developed to reconstruct dynamic MR images, considering the low-rank, global sparsity, gas-inflow effects, and joint sparsity. Both the simulation and the in vivo results verify that the proposed approach outperforms the state-of-the-art methods both in qualitative and quantitative comparisons. In particular, the proposed method acquires 33 frames within 6.67 s (more than double the temporal resolution of the recently proposed strategy), and achieves high-image quality [the improvements are 29.63%, 3.19%, 2.08%, and 13.03% regarding the mean absolute error (MAE), structural similarity index (SSIM), quality index based on local variance (QILV), and contrast-to-noise ratio (CNR) comparisons]. This provides accurate structural and functional information for early detection of obstructive lung diseases.