General but simplified dispersion relation for the lower hybrid wave in low hybrid current drive (LHCD) regime is derived by expanding technique through the small parameter δ=(ω2pe/ω2)-1.The up ward and the downward shifts of the parallel refractive index,and the relevant m ode conversion due to toroidal effects (such as the R-1 dependence of the toroidal magnetic field and the Shafnanov shift of magnetic surfaces) are d iscussed.A sufficient condition for the wave that is possible to penetrate into the inner region of the plasma column is obtained,which has a relationship with the experimentally observed LHCD density limit.A scaling about the critical dens ity is found to be nec∝f4/3Ｂ2/3Ａ4/3,with f,B,A being the wave frequency,the magnetic field and the aspect ratio,r espectively.There exists a quite good agreement between theory and experiments.T he simplified equations for wave propagation can be used as a subroutine in a co mplete LHCD code.