The purpose of this study was to understand how students engage in computer-supported modeling-based activities (CSMBAs), and the relationship between their engagement and their modeling competence. Different facets of learning engagement were measured through multiple data, including performance on modeling tasks, self-reported level of engagement, and online behavior patterns of science modeling. The research participants were 76 11th-grade students in Taiwan. The research instruments included online student worksheets, an engagement questionnaire, computer logs, and modeling competence tests. Students' online worksheets were scored and used to group them into three performance groups--the low-level-performance group (LPG), the middle-level-performance group (MPG) and the high-level-performance group (HPG). ANOVA statistics lag sequential analysis (LSA), and ANCOVA statistics were used for the data analysis. The results showed that, first, in analyzing the engagement questionnaires, students' negative cognitive engagement, negative behavioral engagement, and negative social engagement all played important roles in their low performance in the CSMBAs. Second, through the use of LSA, it was found that the LPG students lacked evaluative behavior, while the HPG students emphasized reflective behavior. Third, analysis of the students' pre- and post-modeling competence tests showed that those who were in the HPG and MPG scored significantly higher than those in the LPG in two dimensions of the modeling competence post-tests. The results indicate that efforts made in completing tasks in CSMBAs can lead to better modeling competence. Implications for developing future CSMBAs and for promoting student engagement are suggested.