In order to improve the ability of the accident prone location identification,the hyperbolic tangent y=a+b×tanh(cx+cd) is proposed as a substitute fitting function of the double exponential function y=a×ebx+c×edx for fitting scatter diagram of accident cumulative frequency.The comparative analysis of the two fitting functions was conducted by simulation analysis and actual data confirmation.The results indicated that the hyperbolic tangent function has higher correlation coefficient in curve fitting,higher detection rate in accident prone location identification,more stable results and better adaptability for the cumulative traffic volume.More significant finding is proposed that the accident number,which decided by cumulative traffic volume in certain accident rate,has very important influence on misdetection rate of accident prone location identification.The hyperbolic tangent can be used for fitting scatter diagram of accident cumulative frequency instead of the double exponential function,and the suggested number of average accident per kilometer should not less than 4 to control the misdetection ratio to about 20%.