Compressed domain image classification performs classification directly on compressive measurements acquired from the single-pixel camera, bypassing the image reconstruction step. It is of great importance for extending high-speed object detection and classification beyond the visible spectrum in a cost-effective manner especially for resource-limited platforms. Previous neural network methods require training a dedicated neural network for each different measurement rate (MR), which is costly in computation and storage. In this work, we develop an efficient training scheme that provides a neural network with dynamic-rate property, where a single neural network is capable of classifying over any MR within the range of interest with a given sensing matrix. This training scheme uses only a few selected MRs for training and the trained neural network is valid over the full range of MRs of interest. We demonstrate the performance of the dynamic-rate neural network on datasets of MNIST, CIFAR-10, Fashion-MNIST, COIL-100, and show that it generates approximately equal performance at each MR as that of a single-rate neural network valid only for one MR. Robustness to noise of the dynamic-rate model is also demonstrated. The dynamic-rate training scheme can be regarded as a general approach compatible with different types of sensing matrices, various neural network architectures, and is a valuable step towards wider adoption of compressive inference techniques and other compressive sensing related tasks via neural networks.