This paper represents a first attempt to apply the concepts of “fractals” to assessment of statistical characteristics in industrial accident occurrence. From the fractal analysis concerning the hierarchic feature in occurrence of hazardous events, it is found that the relationship between the magnitude of damages caused by industrial accidents and their frequencies has a fractal character. As an representation for statistical risk in accident, the reisk curves, in which the exceedance frequencies that magnitude of damages exceeds some given value and its corresponding magnitude of damages are described in the log-log scale, are considered. The risk curve forms a straight line whose gradient is negative in the region of low frequencies and high magnitude of damages, so-called large scale accidents. We can reduce, from the self-simility or scaling property in accident occurrence characteristics depending on magnitude of damages, that the absolute values of slope in the risk curve give the fractal dimension D, and the D is scale invariant and also means the safety index describing the relative level of potential risk for large scale accidents. The implications of results for fractal approachs to risk curves can be proved by statistical examinations using a lot of fire accident insurance data of industrial facilities and installations in Japan.