Quantum Fisher information is a key conception of precision measurement, which determines the precision of the established parameter. In this paper, we give an expression for the quantum Fisher information flow utilizing right logarithmic derivative for open quantum systems and apply it to a two-level system coupled to a non-Markovian environment characterized by Lorentzian spectral density. Discussion of the relation between the sign of quantum Fisher informationflow and the non-Markovianity has been made. In addition, we find the quantum Fisher information flow and the quantum Fisher information show similar behavior. The reason behind this similarity is the null eigenvalue of the density matrix.