Mathematical word problem solving (MWPS) involves multiple steps, including comprehending the problem statements, determining the arithmetic operations that have to be performed, and finding the answers. This study investigated the relative contributions of different cognitive and affective variables to children's MWPS. To achieve this goal, 116 third-grade Chinese children were tested. Results showed that after controlling for age and non-verbal intelligence, the abilities to solve direct and indirect mathematical word problems were positively correlated with the working memory component of executive function, reading comprehension ability, math fact fluency and math anxiety. Moreover, math anxiety was found to fully mediate the relationships between reading anxiety and MWPS. Implications of the findings on how to promote children's MWPS skills were discussed.