As the most efficient renewable energy source for generating electricity in a modern electricity network, wind power has the potential to realize sustainable energy supply. However, owing to its random and intermittent instincts, a high permeability of wind power into a power network demands accurate and effective wind energy prediction models. This study proposes a multi-stage intelligent algorithm for wind electric power prediction, which combines the Beveridge–Nelson (B-N) decomposition approach, the Least Square Support Vector Machine (LSSVM), and a newly proposed intelligent optimization approach called the Grasshopper Optimization Algorithm (GOA). For data preprocessing, the B-N decomposition approach was employed to disintegrate the hourly wind electric power data into a deterministic trend, a cyclic term, and a random component. Then, the LSSVM optimized by the GOA (denoted GOA-LSSVM) was applied to forecast the future 168 h of the deterministic trend, the cyclic term, and the stochastic component, respectively. Finally, the future hourly wind electric power values can be obtained by multiplying the forecasted values of these three trends. Through comparing the forecasting performance of this proposed method with the LSSVM, the LSSVM optimized by the Fruit-fly Optimization Algorithm (FOA-LSSVM), and the LSSVM optimized by Particle Swarm Optimization (PSO-LSSVM), it is verified that the established multi-stage approach is superior to other models and can increase the precision of wind electric power prediction effectively.