In recent years, trustworthiness has garnered increasing attention and exploration in the field of intelligent education, due to the inherent sensitivity of educational scenarios, such as involving minors and vulnerable groups, highly personalized learning data, and high-stakes educational outcomes. However, existing research either focuses on task-specific trustworthy methods without a holistic view of trustworthy intelligent education, or provides survey-level discussions that remain high-level and fragmented, lacking a clear and systematic categorization. To address these limitations, in this paper, we present a systematic and structured review of trustworthy intelligent education. Specifically, We first organize intelligent education into five representative task categories: learner ability assessment, learning resource recommendation, learning analytics, educational content understanding, and instructional assistance. Building on this task landscape, we review existing studies from five trustworthiness perspectives, including safety and privacy, robustness, fairness, explainability, and sustainability, and summarize and categorize the research methodologies and solution strategies therein. Finally, we summarize key challenges and discuss future research directions. This survey aims to provide a coherent reference framework and facilitate a clearer understanding of trustworthiness in intelligent education.