The search for a clean and sustainable energy source has led to a focus on hydrogen as a promising alternative due to its high energy density and zero carbon emissions. Hydrogen production via water electrolysis is a key technology, but efficient catalysts are needed to reduce overpotentials. Noble metals are effective but costly, prompting the development of low-cost catalyst materials. Various hydrogen evolution catalysts have been explored, but traditional methods face challenges in efficiency and randomness. Machine learning has emerged as a powerful tool for rapidly screening and predicting the activity of catalysts, aiding in the discovery of efficient electrocatalysts. Several successful models have been developed to design high-entropy alloy catalysts and predict the activity of different types of hydrogen evolution catalysts with impressive accuracy, using fewer input features. This study focused on developing a machine learning model to design highly active hydrogen evolution catalysts, achieving a high predictive performance with fewer features. By training the model on a dataset of 10,855 hydrogen evolution catalysts, six machine learning models were established, with the Extremely Randomized Trees Regression model outperforming the others. Feature importance analysis and engineering led to the identification of more relevant features, improving the model's accuracy. Comparisons with deep learning models highlighted the importance of feature selection in achieving high predictive performance. The ML model successfully predicted the performance of various hydrogen evolution catalysts, demonstrating its accuracy through validation with DFT methods. This work provides valuable insights for accelerating the design of high-performance hydrogen evolution catalysts.