Accurate prediction for short-term wind speed can reduce the adverse impact of wind farm on power system effectively. To this end, a novel hybrid forecasting approach combining two-layer decomposition, improved hybrid differential evolution-Harris hawks optimization (IHDEHHO), phase space reconstruction (PSR) and kernel extreme learning machine (KELM) is proposed. Primarily, a set of sub-components are obtained by decomposing the collected raw wind speed series with two-layer decomposition strategy. Subsequently, all the sub-components are reconstructed into the corresponding phase space matrixes by PSR, after which the vectors are divided into training, validation and testing sets, respectively. Among the subsets, training set and validation set are applied to establish prediction model and select optimal parameters of KELM. Later, the optimization for arguments within PSR and KELM are synchronously implemented by the proposed IHDEHHO algorithm. Afterward, the final forecast results are deduced by cumulating the forecasting values of all sub-components. Through the application on three datasets collected from Sotavento Galicia (SG) with different prediction horizons and comparison with six related models, it is attested that the proposed hybrid prediction model is effective and suitable for multi-step short-term wind speed forecasting.