Computational thinking (CT) has gained considerable attention and in-depth discussion over the last two decades. Although the significance of CT has been highlighted, it could be challenging for educators to teach CT. Fortunately, adopting robots in education has been evidenced to be of benefit to promoting students’ learning motivation, CT, and higher-order thinking skills. However, several significant factors affecting students’ programming performances in robot-assisted learning activities have been identified, such as cognitive needs and organization. In this study, a CMR-BBP (concept map robot block-based programming) approach was designed by integrating concept maps into robot block-based programming to enhance students’ programming learning. Moreover, a three-group experiment was carried out in an elementary school to evaluate their learning outcomes. The experimental results revealed that the CMR-BBP approach benefited the students’ perceptions of their computational thinking and problem solving in comparison with the R-BBP (robot block-based programming) and C-BBP (conventional block-based programming) approaches. Furthermore, regarding cognitive load, both the CMR-BBP and R-BBP approaches enhanced the students’ germane cognitive load, while the CMR-BBP approach effectively reduced their extrinsic cognitive load. This study could be a notable reference for designing other courses in conjunction with programming learning activities.