Motivation: Protein secondary structure prediction can provide important information for protein 3D structure prediction and protein functions. Deep learning, which has been successfully applied to various research fields such as image classification and voice recognition, provides a new opportunity to significantly improve the secondary structure prediction accuracy. Although several deep-learning methods have been developed for secondary structure prediction, there is room for improvement. MUFold-SS was developed to address these issues. Results: Here, a very deep neural network, the deep inception-inside-inception networks (Deep3I), is proposed for protein secondary structure prediction and a software tool was implemented using this network. This network takes two inputs: a protein sequence and a profile generated by PSI-BLAST. The output is the predicted eight states (Q8) or three states (Q3) of secondary structures. The proposed Deep3I not only achieves the state-of-the-art performance but also runs faster than other tools. Deep3I achieves Q3 82.8% and Q8 71.1% accuracies on the CB513 benchmark.