Interval prediction of wind power, which features the upper and lower limits of wind power at a given confidence level, plays a significant role in accurate prediction and stability of the power grid integrated with wind power. However, the conventional methods of interval prediction are commonly based on a hypothetic probability distribution function, which neglects the correlations among various variables, leading to decreased prediction accuracy. Therefore, in this paper, we improve the multi-objective interval prediction based on the conditional copula function, through which we can fully utilize the correlations among variables to improve prediction accuracy without an assumed probability distribution function. We use the multi-objective optimization method of non-dominated sorting genetic algorithm-II (NSGA-II) to obtain the optimal solution set. The particular best solution is weighted by the prediction interval average width (PIAW) and prediction interval coverage probability (PICP) to pick the optimized solution in practical examples. Finally, we apply the proposed method to three wind power plants in different Chinese cities as examples for validation and obtain higher prediction accuracy compared with other methods, i.e., relevance vector machine (RVM), artificial neural network (ANN), and particle swarm optimization kernel extreme learning machine (PSO-KELM). These results demonstrate the superiority and practicability of this method in interval prediction of wind power.