Based on a stack autoencoder (SAE) combined with an extreme learning machine (ELM), we built a deep neural-network prediction model, SAE-ELM. We initialized and fine-tuned the weights and thresholds of the deep neural networks using the spectral data extracted from the hyperspectral images of apples. Compared with the results of the traditional ELM model, the SAE-ELM determination coefficient of the prediction set increases from 0.7345 to 0.7703, the SAE-ELM residual prediction bias increases from 1.968 to 2.116, and the square root error of the prediction set decreases from 1.6297 to 1.2837. These research results show that the performance of the SAE-ELM model is superior to that of the traditional ELM model, and it is feasible for the proposed model to predict apple firmness.