This paper deals with the existence of positive ω-periodic solutions for the neutral functional differential equation with multiple delays (u(t) − cu(t − δ))′ + a(t)u(t) = f(t, u(t − τ1), . . . , u(t − τn)). The essential inequality conditions on the existence of positive periodic solutions are obtained. These inequality conditions concern with the relations of c and the coefficient function a(t), and the nonlinearity f(t, x1, . . . , xn). Our discussion is based on the perturbation method of positive operator and fixed point index theory in cones.