STEAM contests play a pivotal role in maintaining students' interest and motivation in STEAM education. Finding factors that are related to students' continuance intention (CI) to participate in STEAM contests is important for promoting STEAM education. Previous studies mostly focused on exploring the relationships between students' behavioural attitude, positive affect and their CI for a STEAM contest. However, few studies have explored students' CI from the perspective of help-seeking attitude with the belief-attitude-behaviour model. Thus, this study investigated the relationships among students' hands-on making self-efficacy (HMSE), incremental belief of intelligence (IBI), help-seeking attitudes including instrumental help-seeking (IHS) and executive help-seeking (EHS), and their CI for STEAM contests based on the belief-attitude-behaviour model. A total of 405 elementary and junior high school students who took part in the 2022 STEAM PowerTech contest participated in this study. Structural equation modelling was used for confirmatory analysis to validate the hypotheses. Results indicated that EHS exhibited a negative association with CI, whereas IHS exhibited a positive association with CI. HMSE and IBI were negatively associated with EHS, and positively associated with IHS. This study implies that students with a high level of HMSE and IBI are inclined to exhibit IHS and thus have a strong CI for STEAM contests. The findings provide suggestions on enhancing students' CI for STEAM contests.