This paper proposes an advanced state of function (SOF) estimation algorithm to determine the cranking capability of starting lighting ignition (SLI) battery. This algorithm defines the cranking resistance describing the voltage drop right after the time of cranking. And in order to increase the estimation accuracy against the effect of unpredictable battery parameter changes, a process of online update for cranking resistance is newly proposed by utilizing the specific frequency related to the cranking resistance. The validity of the proposed SOF estimation algorithm along with the online cranking resistance update process is verified by experimental results with LiFePO4 (LFP) battery.