This paper presents a recognition system for understanding the words of home-service-related sign language. Because the data received from a sensor are sequential, the hidden Markov model (HMM) that has been successfully applied to speech signals is chosen as a classifier. However, the number of states in the HMM model should be decided upon first before constructing the HMM classifier. To solve this problem, an entropy-based $K$ -means algorithm is proposed to evaluate the number of states in the HMM model with an entropy diagram. Four real datasets are utilized to verify the developed entropy-based $K$ -means algorithm. Moreover, a data-driven method is given to combine the artificial bee colony algorithm with the Baum–Welch algorithm to determine the structure of HMM. The database contains 11 home-service-related Taiwan sign language words and each word is performed ten times, five males and five females are invited to perform such words. Finally, the recognition system is established by 11 HMM models, and the cross-validation demonstrates an average recognition rate of 91.3%.