Abstract: The relaxation time approximation is an important formalism to deal with the transport phenomena in solid state physics. It is also a frequently applied method in the research of condensed matter physics. The physical background and advantages of the relaxation time approximation is usually missing in many solid-state physics textbooks. Here the mathematical expression is obtained by analyzing the physical process of electron collisions during transport. Then the formal solution of the non-equilibrium distribution function under relaxation time approximation is analytically solved. In this paper concise and logical contents for teaching the relaxation time approxi mation in solid state physics are established，which are helpful for students to fully and deeply understand the related physics and to apply the approximation in the research of condensed matter physics.

Key words:  solid state physics, relaxation time approximation, transport phenomena