This paper is concerned with model reduction for continuous-time linear switched systems with time-varying delay. For a given stable switched system, our attention is focused on construction of a reduced-order model such that the error system is exponentially stable with a prescribed weighted performance. By applying the average dwell time approach and the piecewise Lyapunov function technique, delay-dependent/deley-independent sufficient conditions are proposed in terms of linear matrix inequality (LMI) to guarantee the exponential stability and the weighted performance for the error system. The model reduction problem is solved by using the projection approach, which casts the model reduction problem into a sequential minimization problem subject to LMI constraints by employing the cone complementary linearization algorithm. A numerical example is provided to illustrate the effectiveness of the proposed theory.