The initial carrier-envelope phase dependence of dynamic process for an ultrashort laser pulse propagating non-resonantly in para-nitroaniline (pNA) molecule medium is investigated theoretically, by solving the full Maxwell-Bloch equations. The results show that when the laser pulse propagates with carrier frequency equal to the half of exciting frequency for the molecule’s charge-transfer state, the laser pulse is modulated severely and the population distribution exceeds 1/2 because the two-photon absorption is a resonant process for the interaction of the laser pulse and the dipolar molecule medium. Higher and lower frequencies than carrier frequency occur in the spectrum and even high-order harmonic components approaching to 7th harmonic are produced, forming a continuous spectrum. The sensitivities of the carrier wave reshaping, the high-order harmonic spectrum and the temporal evolution of excited state population to the initial carrier-envelope phase are discussed in detail. It is found that for given pulse width, the phase dependence increases as the laser field grows intense; while for given laser intensity, it decreases when the pulse width becomes narrow. Due to the extra nonlinear effects introduced by the permanent dipole moments of the pNA molecule, the phase sensitivity in this molecule medium is more distinct than in the medium composed of pseudo-molecules without permanent dipole moments.