It is common to use the damage mechanics to study the deformation of fractured rock mass. The geometric damage tensor is always used to describe the effect of distributed joints on mechanical properties of rock mass. The disadvantages of the traditional determination method about geometric damage is that the natural section of rock mass, mining section and the measurement section are not perpendicular to each other. In this paper, a method combining with the probability theory and field scale line method is adopted to determine the geometric damage tensor. This method is convenient and fast. The solution of initial damage in damage evolution equation can be settled with this method. An effective proof is provided for the later analysis of damage stress of fractured rock mass.