Steady-state shear stress（Ք₁₂） and first normal stress difference(N₁) of liquid crystalline polymers at low shear rates were examined by using a mesoscopic constitutive equation set including the idea of initial domain size. For the applicability to the weak shear flow at low shear rates, a Hinch-Leal closure approximation was adopted in the calculation of the constitutive equation set. The steady-state rheological behaviors predicted by adopting the Hinch-Leal approximation were compared with those by the Doi simple decoupling approximation. It could by predicted from the plot of N₁ versus Ք₁₂ that smaller domains distributed isotropically at a quiescent state might maintain the isotropic domain distribution even at the imposition of moderate shear rate, and then could be changed to the ordered (or partially elongated) domain phase by a further increase of shear rate. Such change of the polydomain structure with the increase in shear rate could be proved more precisely by the transient rheological behaviors of N₁ and Ք₁₂ after the start-up of shear flow.