Model Based Predictive Control(MBPC) has been widely used in predictive control since 80's. GPC[1] which is the superset of many MBPC strategies a popular method, but GPC has some weakness, such as insufficient stability analysis, non-applicability to internally unstable systems. However, CRHPC[2] proposed in 1991 overcomes the above limitations. So we chose RHPC based on CRHPC for electric furnace control. An electric furnace which has nonlinear properties and large time delay is difficult to control by linear controller because it needs nearly perfect modelling and optimal gain in case of PID. As a result, those controls are very time-consuming. In this paper, we applied RHPC with equality constraint to electric furnace. The reults of experiments also include the case of RHPC with monotonic weighting improving the transient response and including unmodelled dynamics. So, This paper proved the practical aspect of RHPC for real processes.