Abstract: Mathematical intuition training is one of the main aims of mathematical thinking quality cultivating in college mathematical teaching. It is also the key concern of development of college students- mathematical foundation and mathematical application skills. In this paper, we analyze the relationship between mathematical thinking and mathematical intuition in the view of pedagogy and cognitive psychology, investigate the importance of engineering advanced algebra knowledge for training mathematical intuition of college students and discuss the teaching method according to cognitive structure. Based on the teaching practice of spatial analytic geometry and advanced algebra, we show the importance of mathematical intuition for mathematical thinking of college students by two examples.