The complex rheological behavior of liquid crystalline polymers solutions in the shear flow with perturbations is investigated using the finite volume method.The perturbations of simple shear can be considered as one arising from the addition of a slight extensional component to the velocity gradient.Firstly，the case in the simple shear flow is focused upon

i.e.

the perturbation equal to zero

and some classical solutions can be obtained for various parameter values.This is the preparation for the discussion of perturbation cases

and to check the validity of numerical method.Then

the effect of slight perturbations on the transition to the flow type of liquid-crystalline polymers (LCPs) is explored in detail.Results indicate that the mechanism of transformation is different for low and high shear rates.Finally

rheological predictions and some micro properties of orientation are also obtained from the perturbation system

and the results show that the effect of perturbations in flow type can also significantly change the related material functions.