This note concerns delay-dependent robust stability criteria and a design method for stabilizing neutral systems with time-varying structured uncertainties. A new way of deriving such criteria is presented that combines the parameterized model transformation method with a method that takes the relationships between the terms in the Leibniz-Newton formula into account. The relationships are expressed as free weighting matrices obtained by solving linear matrix inequalities. Moreover, the stability criteria are also used to design a stabilizing state-feedback controller. Numerical examples illustrate the effectiveness of the method and the improvement over some existing methods.