Abstract: This paper proposes a conformable fractional-order grey system model abbreviated as CFGM(\alpha,\gamma), which is an extension of the integer-order GM(1,1) model. The explicit expressions of the time response function and the restored values are derived by defining the conformable fractional-order derivative and accumulation. By using the least square estimation method, linear system parameters are derived, and then the ant lion optimizer algorithm is applied to search nonlinear system parameters. The effectiveness and feasibility of the CFGM(\alpha,\gamma) model are verified with seven-time series of the M3-Competition. Finally, the new model is applied to the electricity consumption of China. With data from 2009 to 2018, we establish 21 subcases for each selected province and calculate its overall performance, which shows that the new model is more stable than the GM(1,1) and FGM(q,1) models and can obtain competitive results.