We present an exposure-time calculator (ETC) for the Immersion Grating Infrared Spectrograph (IGRINS). The signal and noise values are calculated by taking into account the telluric background emission and absorption, the emission and transmission of the telescope and instrument optics, and the dark current and read noise of the infrared detector arrays. For the atmospheric transmission, we apply models based on the amount of precipitable water vapor along the line of sight to the target. The ETC produces the expected signal-to-noise ratio (S/N) for each resolution element, given the exposure-time and number of exposures. In this paper, we compare the simulated continuum S/N for the early-type star HD 124683 and the late-type star GSS 32, and the simulated emission line S/N for the H2 rovibrational transitions from the Iris Nebula NGC 7023 with the observed IGRINS spectra. The simulated S/N from the ETC is overestimated by 40-50% for the sample continuum targets. ; Comment: 27 pages, 11 figures, Accepted to be published in Advances in Space Research (JASR)