Extreme learning machine (ELM) is a recently proposed learning algorithm for single-hidden-layer feedforward neural networks, which has a fast learning speed while avoiding the problem of local optimal solution. However, the performance of ELM may be affected due to the random determination of the input weights and hidden biases. In this paper, a multi-objective optimized extreme learning machine (MO-ELM) is proposed to solve this problem. The algorithm uses the no-dominated sorting genetic algorithm II algorithm to select input weights and hidden biases. Both the learning errors and the mean square value of output weights are used as optimization objects. The MO-ELM algorithm is used in the multi-step forecast of irregular complex flow oscillations of natural circulation system in rolling motion, and the influences of learning errors and output weights on forecast results are analyzed. Experimental results show that MO-ELM can achieve good generalization performance with much more compact networks and provide a relatively accurate forecast method of flow rate, and the forecast results can be used as reference to nuclear power system operators.