In this study, we consider a nonlinear neutral-type system with periodic coefficients and variable delay. We obtain some new estimates to characterize the exponential decay of solutions of the system as t -> +infinity. A Lyapunov-Krasovskii functional is defined to prove the results of this work. An example is given to show applicability of the established assumptions by MATLAB-Simulink. The obtained results extend and generalize the existing ones in the related literature.