The locally rotationally symmetric (LRS) Bianchi type-Ⅱ inflationary cosmological model is investigated for massless scalar field with fiat potential and time varying A.To obtain the deterministic solution,it is assumed that scale factor is a(t)～eHt as we considered previously for Bianchi type-I spacetime and A～a-2 as considered by Chen and Wu,where H is the Hubble constant and effective potential V(φ)=const; φ Higgs field. It is shown that such a time varying A leads to no conflict with existing observations.However,it does change the predictions of standard cosmology in the matter-dominated phase and alleviates some problems in reconciling observations with the inflationary scenario.The model represents anisotropic spacetime in general.However,the model isotropizes for large values of t and β =3H2,where β is constant.The physical and geometrical aspects of the model in the context of an inflationary scenario is also discussed.