Rheometry testing and the DSC measurement of five thermotropic liquid crystalline polymers (TLCP) have been carried out. The dynamic viscosities of the five TLCPs show a typical shear-thinning behaviour obeying the power-law with the power indices from 0.2 to 0.3. When these TLCPs are heated above the melting temperatures determined by the DSC measurements, the dynamic viscosities first rapidly decrease by 2～3 orders of magnitude then level off, finally increase gradually with the further increasing of temperature. The steady shearing exhibited the same behaviour as the dynamic shearing, but serious edge fracture of material slippage out of the plates occurred. The abnormal temperature dependence of the viscosities can be explained by the nematic-isotropic transition. By using the concept of activation energy, we propose a simple model which can fit the shear-thinning behaviour quite well and predict qualitatively correct temperature effects.