Local structure prediction can facilitate ab initio structure prediction, protein threading, and remote homology detection. However, previous approaches to local structure prediction suffer from poor accuracy. In this paper, we propose a knowledge-based prediction method that assigns a measure called the local match rate to each position of an amino acid sequence to estimate the confidence of our approach. To remedy prediction results with low local match rates, we use a neural network prediction method. Then, we have a hybrid prediction method, HYPLOSP (HYbrid method to Protein LOcal Structure Prediction) that combines our knowledge-based method with a neural network method. We test the method on two different structural alphabets and evaluate it by QN, which is similar to Q3 in secondary structure prediction. The experimental results show that our method yields a significant improvement over previous studies.