With the slow effect of electric field of thundercloud, a kind of positive glow corona without streamers is initiated from the surface of object near the ground, and a large number of positive space charges are injected into the surrounding space, consequently, lighting targets selected by the lighting leader can be changed. In this paper, a numerical simulation of positive glow corona discharge initiated from the long ground wire with the effect of the electric field of thundercloud is presented. In consideration of the attachment and collision effects between positive ions and other ions, an accurate two-dimensional positive glow corona model is established. Meanwhile, a high-voltage corona discharge experiment is done in the laboratory to measure the corona current in different background electric fields, and the results are compared with the simulation results in order to verify the correctness of the model established in this paper. According to the established model, the initiation and development progress of glow corona with the effect of thundercloud are simulated and the corona current, laws of positive ion density distribution and migration are revealed. Results show that positive ions generated from the glow corona discharge present a circular symmetric distribution in the plane perpendicular to the ground wire at their early stage of migration, but the distribution is shaped as an elongated oval later when the ions move farther from the ground wire for the effect of electric field of thundercloud, that is to say, the overwhelming majority of the ions will be finally distributed in the upper area of the ground wire and gradually migrate towards the thundercloud. Due to the accumulation effects of positive ions in the upper migration area near the ground wire, the positive space charge background is formed, which has a damping effect on the electron beam. Thus the formation of electron avalanche is suppressed and the probability for electron avalanche to be converted into streamer is reduced. Meanwhile, the positive space charge background improves the collision surface of the gas and increases the compound probability between positive ions and electrons. Therefore, the conversion processes from electron avalanche and streamer to upward leader are impeded and the initiation of upward leader is suppressed.