Abstract: Coronal Mass Ejections （CMEs） are important factors for the space weather. The geomagnetic storms with sudden commencement are caused by CMEs. CMEs with the south direction of B_z ＞ 10 nT and high traveling speed can often cause intensive magnetic storm. But many problems keep unsolved on the relationship between a CME and the intensity of the relative geomagnetic storm. In this paper, the traveling directions of several coronal mass ejections causing severe geomagnetic storm are investigated by using the galactic cosmic ray data observed at McMurdo and Thule neutron monitor. If a CME’s traveling direction straightly towards to magnetopause, then the variation in galactic cosmic ray intensity observed at the two stations should be almost the same. Several selected CME events are analyzed. The results show that the direction of the CME related to the geomagnetic storm on Dec.19, 1980 was almost dead against magnetopause, the situation was the same for the CMEs related to the geomagnetic storms on Jul.13, 1982, Nov.6, 2001 and Mar.31, 2001. The traveling direction of the CME related to the geomagnetic storm on Jul.15, 2000 is slightly directed to south of the earth. By comparing the intensity of the geomagnetic storm on March 31, 2001 and July 15, 2000 and comparing the disturbed solar wind driven by corresponding CME, it is thought that the traveling direction of a CME is a factor having impact on the intensity of the geomagnetic storm caused by the CME. For a CME, the more deflection of its traveling direction towards the magnetopause, the weaker the geomagnetic storm caused by it.