Electricity price forecast is of great importance to electricity market participants. Given the sophisticated time-series of electricity price, various approaches of extreme learning machine (ELM) have been identified as effective prediction approaches. However, in high dimensional space, evolutionary extreme learning machine (E-ELM) is time-consuming and difficult to converge to optimal region when just relying on stochastic searching approaches. In the meanwhile, due to the complicated functional relationship, objective function of E-ELM seems difficult also to be mined directly for some useful mathematical information to guide the optimum exploring. This paper proposes a new differential evolution (DE) like algorithm to enhance E-ELM for more accurate and reliable prediction of electricity price. An approximation model for producing DE-like trail vector is the key mechanism, which can use simpler mathematical mapping to replace the original yet complicated functional relationship within a small region. Thus, the evolutionary procedure frequently dealt with some rational searching directions can make the E-ELM more robust and faster than supported only by the stochastic methods. Experimental results show that the new method can improve the performance of E-ELM more efficiently.