Although the relations between executive functions and academic achievement are considered widely proven, due to the methodological limitations of most studies little can be said about the relational importance of various executive functions for achievements in math, reading, and writing. Therefore, this study aimed to examine the role of different executive functions postulated by Miyake et al. (2000) (response inhibition, working memory updating, and mental set shifting) on academic achievements in math, reading, and writing as well as the possible mediation effects of cognitive (verbal and performance intelligence) and behavioral variables (learning-related behavior and hyperactivity). In total, 101 children were tested in the second grade of a primary school on nine simple computer tasks intended to predominantly tap one of the three executive abilities: response inhibition, mental set shifting, and working memory updating. In addition, all participants completed the Wechsler Abbreviated Scale of Intelligence (WASI). The construct validity of the executive function tasks was established by a confirmatory factor analysis: consistent with other latent variable studies of executive function, the three target executive abilities proved to be separable and moderately correlated with each other (Miyake et al., 2000; Rose et al., 2011). Academic achievement was evaluated by a teacher’s report. The research variables of hyperactivity and learning-related behavior were composed using teachers’ answers to the questions from the Hyperactivity Scale of Strengths and Difficulties Questionnaire (SDQ) and the parents’ and teachers’ answers to additional questions concerning children’s learning-related behavior. Structural equation modelling was used to examine the structural relations of predictors (latent factors of response inhibition, memory updating, and mental set-shifting), mediators (verbal intelligence, performance intelligence, hyperactivity, and learning-related behavior) and dependent variables (math, reading and writing achievement scores). Executive functions proved to be important predictors of academic achievement in primary school. Working memory updating was directly related to achievements in reading (beta = 0.69, p = 0.04) and writing (beta = 0.71, p = 0,01). Response inhibition and mental set-shifting were related to math achievement through behavioral mediators: children with a better ability to regulate inappropriate responses showed fewer symptoms of hyperactivity (beta = -0.42, p = 0.05), which in turn led to higher achievements in math (beta = -0.40, p = 0.001); children with better mental set-shifting demonstrated more appropriate learning-related behaviors (beta = 0.49, p = 0.05), while learning-related behaviors also predicted math achievements (beta = 0.26, p = 0,04). In contrast, verbal and performance intelligence did not have any significant relation to academic achievements in primary school.