The grey system model with time power, which is often called the GM, appeals considerable interest of research due to its effectiveness in time series forecasting. Aimed to improve further the GM model, this paper introduces a new whitening equation with variable coefficient into the original whitening equation which extends applicable scope; as a result, an improved grey model with time power, namely, OGM, is proposed. Firstly, the time response function of the novel model and the restored values of original (...) series are deduced through grey modelling techniques. Secondly, the variable coefficient in the whitening equation and the time power are determined by particle swarm optimization algorithm. Two empirical examples are then used to verify the validity of the novel model. Finally, the novel model is applied to predict the oil consumption of China from 2004 to 2018. Results show the novel model outperforms other commonly-used competitive models, which can well serve a benchmark model for scholars and decision-makers. (shrink)