ARGO-YBJ, located at the Yangbajing cosmic ray Observatory (4300 m a. s. l., Tibet, China), has a threshold energy of about several hundred GeVs. It is particular useful in searching for high energy GRBs because of its unique advantages of high altitude, wide field of view, and full coverage. ARGO-YBJ experiment can not distinguish between photons and protons. To find photon signals in a large number of cosmic ray events, we must correctly estimate the background event rate, which is the key to search for high-energy GRBs. In this paper, the “equi-zenith-angle” method is used to analyze the cosmic ray background of GRBs in ARGO experiment. Due to the rotation of the earth, the zenith angle varies with time. We focuses on the analysis of the change of zenith angle in the duration of the long GRBs, so that the background estimation is more accurate.