We have investigated the relationship between the polar anchoring energy and the surface order parameter in nematic liquid crystal (NLC), 4-n-pentyl-4-cyanobiphenyl (5CB), on the two kinds of the weakly rubbed polyimide (PI) surfaces. The observed polar anchoring energy of 5CB is approximately 2${ imes}10^{-4}(J/m^2$) and then increases with increasing the rubbing strength (RS) on weakly rubbed surface (RS=57mm) with side chain at $30^{circ}C$; same results are obtained on weakly rubbed PI surface without side chain. The surface order parameter of 5CB on rubbed PI surfaces increases with increasing the RS at a weak rubbing region. The surface order parameter of 5CB is strongly related to the characteristics of PI material. Consequently, we suggest that the polar anchoring energy of NLC is strongly attributed to the surface order parameter on rubbed PI surfaces.