Deep learning-based informative band selection methods on hyperspectral images (HSI) recently have gained intense attention to eliminate spectral correlation and redundancies. However, the existing deep learning-based methods either need additional post-processing strategies to select the descriptive bands or optimize the model indirectly, due to the parameterization inability of discrete variables for the selection procedure. To overcome these limitations, this work proposes a novel end-to-end network for informative band selection. The proposed network is inspired by the advances in concrete autoencoder (CAE) and dropout feature ranking strategy. Different from the traditional deep learning-based methods, the proposed network is trained directly given the required band subset eliminating the need for further post-processing. Experimental results on four HSI scenes show that the proposed dropout CAE achieves substantial and effective performance levels outperforming the competing methods.