The stability and stabilization of a class of linear switched time-varying delay systems are investigated.A piecewise quadratic Lyapunov function (PWQLF) is constructed and is used to obtain the stability conditions based on the linear matrix inequalities (LMIs).The stabilizing controller for this class of system is then designed and the solution of the desired controller can be obtained by a cone complementary linearization algorithm.Numerical examples are provided to illustrate the less conservativeness of the new stability and the validity of the controller design procedures.