The present study investigated the role of both cognitive and linguistic predictors in basic arithmetic skills (i.e., addition and subtraction) in 69 first-language (L1) learners and 60 second-language (L2) learners from the second grade of primary schools in the Netherlands. All children were tested on non-verbal intelligence, working memory, phonological awareness, grammatical ability as well as basic arithmetic skills. The L2 learners scored lower than L1 learners on phonological awareness, grammatical ability, and basic arithmetic skills (i.e., addition and subtraction), but not on non-verbal intelligence and working memory. For both groups, the same precursors applied to the variation in basic arithmetic skills. In addition to non-verbal intelligence and working memory, both phonological awareness and grammatical ability predicted basic arithmetic skills, indicating that assessment of arithmetic problems in L1 learners and L2 learners should take into account the cognitive and linguistic abilities that children bring to the classroom.