In this paper, a new feedback control technique called periodic output feedback is investigated in the context of infinite-dimensional linear systems modeled by neutral functional differential equations, In this method, discrete output samples are multiplied by a periodic gain function to generate a continuous feedback control. This work focuses on stabilization of neutral systems with delayed control modeled in the state space W-2((1))([ - tau,0];R(n))xL(2)([ - tau,0],R(R)), where W-2((1))([ - tau,0];R(n)) denotes the Sobolev space of R(n)-valued, absolutely continuous functions with square integrable derivatives on [- tau, 0]. We show that a class of these systems can be stabilized by periodic output feedback, even though their input operators are unbounded, We overcome this difficulty by representing the system state using an abstract integral "variation of constants" formula. An algorithm is presented at the end of this paper to construct a periodic output feedback gain function. An example is provided to illustrate the construction of the gain function.