The effective dielectric response of linear composites containing graded material is investigated under an applied electric field Eo. For the cylindrical inclusion with gradient dielectric function, εi(r) = b+cr, randomly embedded in a host with dielectric constant εm, we have obtained the exact solution of local electric potential of the composite media regions, which obeys a linear constitutive relation D= εE, using hypergeometric function. In dilute limit, we have derived the effective dielectric response of the linear composite media. Furthermore, for larger volume fraction, the formulas of effective dielectric response of the graded composite media are given.