The secondary structure prediction of proteins is a classic topic of computational structural biology with a variety of applications. During the past decade, the accuracy of prediction achieved by state-of-The-Art algorithms has been 80%; meanwhile, the time cost of prediction increased rapidly because of the exponential growth of fundamental protein sequence data. Based on literature studies and preliminary observations on the relationships between the size/homology of the fundamental protein dataset and the speed/accuracy of predictions, we raised two hypotheses that might be helpful to determine the main influence factors of the efficiency of secondary structure prediction. Experimental results of size and homology reductions of the fundamental protein dataset supported those hypotheses. They revealed that shrinking the size of the dataset could substantially cut down the time cost of prediction with a slight decrease of accuracy, which could be increased on the contrary by homology reduction of the dataset. Moreover, the Shannon information entropy could be applied to explain how accuracy was influenced by the size and homology of the dataset. Based on these findings, we proposed that a proper combination of size and homology reductions of the protein dataset could speed up the secondary structure prediction while preserving the high accuracy of state-of-The-Art algorithms. Testing the proposed strategy with the fundamental protein dataset of the year 2018 provided by the Universal Protein Resource, the speed of prediction was enhanced over 20 folds while all accuracy measures remained equivalently high. These findings are supposed helpful for improving the efficiency of researches and applications depending on the secondary structure prediction of proteins.