Abstract: An interval matrix is constructed to transform the switched linear system into interval system. Then, a sufficient condition is presented in terms of matrix inequality for the quadratic stability of switched linear systems under any switching laws. This condition is equivalent to the critical condition for common quadratic Lyapunov function to all subsystems, while it is much simpler than the latter because it needs only one matrix inequality to solve but the latter involves several LMIs with immense computation to do if there are not a few subsystems. A numerical example illustrates the effectiveness of the method.