© 2016. The American Astronomical Society. All rights reserved.. Cosmological hydrodynamic simulations can accurately predict the properties of the intergalactic medium (IGM), but only under the condition of retaining the high spatial resolution necessary to resolve density fluctuations in the IGM. This resolution constraint prohibits simulating large volumes, such as those probed by BOSS and future surveys, like DESI and 4MOST. To overcome this limitation, we present "Iteratively Matched Statistics" (IMS), a novel method to accurately model the Lyα forest with collisionless N-body simulations, where the relevant density fluctuations are unresolved. We use a small-box, high-resolution hydrodynamic simulation to obtain the probability distribution function (PDF) and the power spectrum of the real-space Lyα forest flux. These two statistics are iteratively mapped onto a pseudo-flux field of an N-body simulation, which we construct from the matter density. We demonstrate that our method can reproduce the PDF, line of sight and 3D power spectra of the Lyα forest with good accuracy (7%, 4%, and 7% respectively). We quantify the performance of the commonly used Gaussian smoothing technique and show that it has significantly lower accuracy (20%-80%), especially for N-body simulations with achievable mean inter-particle separations in large-volume simulations. In addition, we show that IMS produces reasonable and smooth spectra, making it a powerful tool for modeling the IGM in large cosmological volumes and for producing realistic "mock" skies for Lyα forest surveys.