Atrial fibrillation (AF) is the most common cardiac arrhythmias in clinic, it is characterized by multiple waves of excitation coursing through myocardial tissue. AF disrupts the normal sinus rhythm and may arise from ectopic foci. In right atrium, there are many different conduction bundles which have different action potential morphology, and they provide a substrate for reentrant activity during AF. Fibre orientation is important in electric propagation and maintaining AF, however, most previous simulation studies didn't consider the fibre orientation. In this paper we studied the effect of tissue heterogeneity and anisotropy on initiation and maintaining of AF based on a realistic human atrial model with fibre orientation and detailed conduction system. The results showed that tissue heterogeneity and anisotropy are important for AF, and in some cases AF is transient due to the lack of anisotropy. Fiber orientation is very important in sustaining of re-entry waves. This investigation suggests that a detail atrial anatomical model should be necessary for AF simulation.