The existence of periodic solutions for the type of generalized Lienard functional differential equations x"(t) + f(x(t))x'(t) + a(t)g(x(t)) + b(t)x(t) = p(t) with higher-order iteration is studied by means of the methods based on topological degree theory, and on conditions that f is bounded or unbounded, sufficient condition for the equation with periodic solutions is obtained respectively.