This study analyzes the explanatory power of cognitive components for the difficulty of national algebra test items. According to four cognitive components including the type of number, representation transformation, computational complexity, and equation information, a total of 65 algebra test items were drawn from the Basic Competence Test and the Comprehensive Assessment Program for Junior High School Students administered in Taiwan over the past ten years. A total of 982 students in the ninth grade were tested. The Rasch model is used to adjust the difficulty parameters, and the multivariate regression is used to predict and analyze the difficulty parameters of the test components. The results show that representation transformation, computational complexity, and equation information explain the difficulty parameter of the test items by about 82%. The initial trial indicates that the proposed algebraic cognitive components provide a reasonable explanation for the difficulty of the test items. Researchers and teachers can apply these components as the basis for algebra teaching and the testing design and planning for the supplementary algebra learning materials.