This paper proposes a novel recurrent multi-steps-prediction model call Recurrent Kernel Online Sequential Extreme Learning Machine with Surprise Criterion (SC-RKOS-ELM). This model combines the strengths of Kernel Online Sequential Extreme Learning Machine (KOS-ELM), the characteristics of surprise criterion and advantages of recurrent multi-steps-prediction algorithm to unleash the restriction of prediction horizon and reduce the computation complexation of the learning part. In the experiment, we employ two synthetic and two real-world data sets, including Mackey-Glass, Lorenz, palm oil price and water level in Thailand, to evaluate Recurrent Online Sequential Extreme Learning Machine (ROS-ELM) and Recurrent Kernel Online Sequential Extreme Learning Machine with Fixed-budget Criterion (FB-RKOS-ELM). The results of experiments indicate that SC-RKOS-ELM has the superior predicting ability in all data sets than others.