This paper is concerned with the problem of model reduction for neutral-type control system. For a given stable neutral-type control system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well in a robust performance but is also translated into a linear lower-dimensional system. Sufficient condition is proposed for the asymptotic stability with an error performance for the error system. Then, the model reduction problem is solved by using the projection approach, which casts the model reduction subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Moreover, by further extending the results, model reduction with special structures is obtained, i.e., no neutral-type model. A numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed controller design approach.