Local structure prediction can facilitate ab initio structure prediction, protein threading, and remote homology detection. However, the accuracy of existing methods is limited. 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 method. Empirically, the accuracy of the method correlates positively with the local match rate; therefore, we employ it to predict the local structures of positions with a high local match rate. For positions with a low local match rate, we propose a neural network prediction method. To better utilize the knowledge-based and neural network methods, we design a hybrid prediction method, HYPLOSP (HYbrid method to Protein LOcal Structure Prediction) that combines both methods. To evaluate the performance of the proposed methods, we first perform cross-validation experiments by applying our knowledge-based method, a neural network method, and HYPLOSP to a large dataset of 3,925 protein chains. We test our methods extensively on three different structural alphabets and evaluate their performance by two widely used criteria, Maximum Deviation of backbone torsion Angle (MDA) and Q(N), which is similar to Q(3) in secondary structure prediction. We then compare HYPLOSP with three previous studies using a dataset of 56 new protein chains. HYPLOSP shows promising results in terms of MDA and Q(N) accuracy and demonstrates its alphabet-independent capability.