Background: When mathematical knowledge is expressed in general language, it is called verbalized mathematics. Previous studies on verbalized mathematics typically paid attention to mathematical vocabulary or educational practice. However, these studies did not exclude the role of symbolic mathematics ability, and almost no research has focused on verbalized mathematical principles. Aims: This study is aimed to investigate whether verbalized mathematics ability independently predicts mathematics achievement. The current study hypothesized that verbalized mathematics ability supports mathematics achievement independent of general language, related cognitive abilities and even symbolic mathematical ability. Sample: A sample of 241 undergraduates (136 males, 105 females, mean age = 21.95, SD = 2.38) in Beijing, China. Methods: A total of 12 tests were used, including a verbalized arithmetic principle test, a mathematics achievement test, and tests on general language (sentence completion test), symbolic mathematical ability (including symbolic arithmetic principles test, simple arithmetic computation and complex arithmetic computation), approximate number sense ability (numerosity comparison test) and several related cognitive covariates (including the non-verbal matrix reasoning, the syllogism reasoning, mental rotation, figure matching and choice reaction time). Results: Results showed that the processing of verbalized arithmetic principles displayed a significant role in mathematics achievement after controlling for general language, related cognitive abilities, approximate number sense ability and symbolic mathematics ability. Conclusions: The results suggest that verbalized mathematics ability was an independent predictor and provided empirical evidence supporting the verbalized mathematics role on achievement as an independent component in three-component mathematics model.