Wind power point and interval prediction plays an important role in dispatching. However, for obtaining both point estimations and prediction intervals (PIs), the existing models like constructing the probability density function are too complicated. This paper proposes a novel multi-objective upper and lower bound and point estimation (MOULPE) model. It constructs a neural network (NN) with double outputs to directly estimate the prediction intervals (PIs) and the median of PIs is calculated as point estimation. Considering wide decision-making space, the problem formulation of MOULPE is defined as three objectives which covers both evaluation indices of PIs and point prediction. Furthermore, based on elite opposition-based learning (EOBL), this paper improves non-dominated fast sort genetic algorithm-III (INSGA-III) to search the optimal front. Two criteria called prediction interval nominal confidence (PINC) and point prediction nominal error (PPNE) are adopted to pick out the best solution. According to the general requirements in literature, four examples of real wind power data are conducted. Compared with some state-of-the-art methods, the coverage probability of PIs constructed by the proposed model not only reaches the preset PINC, but the average width is also the lowest. Similarly, the point estimation error of the proposed method is less than PPNE.