This study explored whether executive functioning skills and maths test anxiety were associated with children’s untimed and timed algorithmic computational performance and their discrepancy. It also investigated whether such relations were moderated by children’s basic maths fact fluency. One hundred and thirty third-graders were rated by teachers regarding their executive functioning skills. Moreover, they self-reported their maths test anxiety level and were tested on various maths skills. Results showed that for untimed computational performance, working memory was a correlate among children low in basic maths fact fluency, whereas maths test anxiety was a correlate among all children. Planning/organization and maths test anxiety were correlates of timed computational performance, regardless of the basic maths fact fluency level. As for discrepancy in computational performance across the two conditions, maths test anxiety was a correlate among children low in basic maths fact fluency. Implications on how to promote children’s algorithmic computation were discussed.