In recent years, quantifying non-Markovian effect in open quantum systems has become an important problem in the quantum decoherence control field. In this paper, a non-Markovian measure of independent of the initial state of open systems is proposed, which is based on quantum Fisher information extended from the case of the initial pure state of the system to that of the general mixed state of the system. As its application, the non-Markovian processes are quantified by quantum Fisher information for a two-level system undergoing the three famous dissipative channels, such as amplitude dissipative channel, phase damping channel and random unitary channel, respectively. The results show that the conditions of non-Markovian processes in the three dissipative channels are independent of the selection of the initial state of the system by means of the quantum Fisher information of a phase parameter. Further, for amplitude dissipation channel and phase damping channel, the conditions for the occurrence of non-Markovian processes are equivalent to those given by trace distance, divisibility, quantum mutual information and quantum Fisher-information matrix et al. As expected, for the case of amplitude dissipation channel the corresponding results can reduce to the one in other papers by selecting initial state of the system as the optimal pure state. However, for random unitary channel, the conditions of non-Markovian processes are not equivalent to other measures. In addition, we also obtain an interesting relationship in the three dissipative channels between quantum Fisher information and quantum coherence of the open systems, namely the square of quantum <i>l</i><sub>1</sub> coherence for the evolved state of system is exactly equal to the quantum Fisher information of the phase parameter. In a word, the obtained results of independent of the initial state of open systems for the quantifier of non-Markovian process not only improve the application scope of quantum Fisher information to detect non-Markovian effect in open systems, but also further highlights its important role in quantum information processing.
