The open-circuit voltage (OCV) of a battery, as a crucial characteristic parameter, is widely used in many aspects of battery technology, such as electrode material mechanism analysis, battery performance/state estimation and working process management. However, the applications of OCV are severely limited due to the need for a long rest time for full relaxation. In this paper, a rapid OCV prediction method is proposed to predict the final static OCV in a few minutes using linear regression techniques, based on a new mathematical model developed from an improvement on a second-order resistance–capacitance (RC) model. As the improvement, an important discovery is demonstrated by experimental investigation and data analysis: the relaxation time (i.e., time constant) of the diffusion circuit of the second-order RC model is not a fixed constant, unlike an intrinsic value for a given material, but an apparent linear function of the open-circuit time. This improvement enables the new model to track the actual relaxation process very well. The accuracy and the rapidity of the new model and proposed method are validated with working-condition experimental data on battery cells with different cathodes, and the results of OCV prediction are very accurate (errors below 1 mV in 20 min).