In this paper，the coefficient of thermal expansion of aluminum and copper metals is obtained by calculating the lattice constants，binding energy and Debye temperature via the density functional method based on quantum mechanics. Experimental design and data measurement are also carried out. Moreover，the theoretical simulation values are compared with the experimental results achieved by using an optical lever. The error sources were analyzed and the experimental methods for improving the errors were proposed. The results should provide reference for the future experimental design and theoretical simulation of metal thermal expansion coefficient in university physics courses.