We propose the daily computed weighted averaging basic reproduction number 𝑅_(0,𝑘,𝜔)^𝑛 for Middle East respiratory syndrome coronavirus (MERS-CoV) outbreak in South Korea, May to July 2015. We use an SIR model with piecewise constant parameters β (contact rate) and γ (removed rate). We use the explicit Euler’s method for the solution of the SIR model and a nonlinear least-square fitting procedure for finding the best parameters. In 𝑅_(0,𝑘,𝜔)^𝑛 the parameters 𝑛, 𝑘 and 𝜔 denote days from a reference date, the number of days in averaging, and a weighting factor, respectively. We perform a series of numerical experiments and compare the results with the real-world data. In particular, using the predicted reproduction number based on the previous two consecutive reproduction numbers, we can predict the future behavior of the reproduction number.