Discharge analysis technique for dielectric liquid was presented by using the Finite Element Analysis (FEA) under a lightning impulse incorporating two-phase flow phenomena which described gas and liquid phases in discharge space. Until now, the response of step voltage has been extensively explored, but that of lightning impulse voltage was rarely viewed in the literature. We, therefore, developed an analyzing technique for dielectric liquid in a tip-sphere electrode stressed by a high electric field. To capture the bubble phase, the Heaviside function was introduced mathematically and the material functions for the ionization, dissociation, recombination, and attachment were defined in liquid and bubble, respectively. By using this numerical setup, the molecular dissociation and ionization mechanisms were tested under low and high electric fields resulted from the lightning impulse voltage of 1.2/50 ${mu}s$. To verify our numerical results, the velocity of electric field wave was measured and compared to the previous experimental results which can be viewed in many papers. Those results had good agreement with each other.