The aim of this paper is to design a discrete-time LQG dynamic controller directly from the Markov parameters of a linear time-invariant plant. The main result obtained states that such a controller can be completely designed using only Markov parameters of the plant, and the designed controller is obtained in the form of its Markov parameters. This leads to a nonparametric design methodology based on the plant input-output behavior, and does not require a state-space realization of the plant. As an illustrative example, a reduced-order sampled-data controller is successfully designed for an infinite-dimensional time-delay plant.