According to self-determination theory, teachers' autonomy support is an effective approach to motivate students to learn. Longitudinal studies are necessary to clear up the relation between students' perception of teacher autonomy support and students' achievement in mathematics. The present study investigated the effect of teachers' autonomy support on students' maths achievement over three years using a longitudinal survey in Chinese elementary schools. Structural equation modelling was employed to explore the complex mechanism of autonomy-supportive teaching on students' mathematics achievement. The results show that teachers' autonomy support can satisfy students' psychological needs, which can enhance their motivation and ultimately positively related with their mathematics achievement. It is worth noting that the students' satisfaction of psychological needs for autonomy and intrinsic motivation have not only a direct effect but also lagged effect. These findings have theoretical and practical significance for mathematics teaching.