An analytical model of black hole (BH) evolution is proposed by considering the Blandford-Znajek process with a transient magnetized accretion disc, which is used as a central engine for powering gamma ray bursts (GRBs). The state of BH evolution can be described by the representative points in the corresponding sub-regions of a parameter space. It is shown that the BH spin might be spun up rather than slowed down, provided that the ratio of the angular velocity of the magnetic field lines to that of the BH horizon is greater than a critical value. In addition, the effects of some initial values of the BH system on the evolution terminals and the output energy for GRBs are discussed in the parameter space.