In this paper, the existence of nonoscillatory solutions for a class of higher-order nonlinear differential equations is investigated. Notably, the equations are of mixed neutral type with a forcing term, which distinguished the equations in this paper from the existing ones and made the qualitative analysis of the solution more complicated. By means of the Schauder-Tychonoff fixed point theorem and inequality techniques, some new sufficient conditions for the existence of nonoscillatory solutions were established. The results in this paper improved and generalized some known results in the existing works. Finally, an example was given to illustrate the effectiveness of the proposed method.