This study examined the associations between school entry skills and science achievement at both the student and school levels among fourth-grade students in South Korea, Singapore, Japan, Chinese Taipei, and Hong Kong. Data of the five Asian regions in the 2015 Trends in International Mathematics and Science Study (TIMSS) were analysed. Variables included Interest, Self-concept, School entry skills - reported by parents, Cognitive activities, Parent attitudes toward mathematics and science, Home educational resources, and Gender, all at the student level, and Emphasis on academic success, Discipline problems, and School entry skills -- reported by principals at the school level. Results of the multilevel path analysis indicated that School entry skills positively and directly influenced science achievement, and simultaneously mediated the influence from cognitive activities to science achievement at the student level. These findings were consistent among the five Asian regions. At the school level, it was found that compared to School entry skills, School emphasis on academic success was the stronger predictor of science achievement among students for most Asian regions. Implications for improving primary school students' science learning are discussed.