The paper derives a mathematical expression on the basis of the probability theory for the time from one earthquake to the next earthquake ( waiting time)，and gives the waiting time expressions in terms of Weibull distribution，exponential distribution，and uniform distribution． We take Hebei Province and its adjacent area as an example，and the three distribution functions are calculated for the waiting time probability of earthquakes with M≥5． 0 in the regions in future and the kind of distribution function is more suitable for the North China area． the M≥5． 0 earthquake hazard analysis are discussed using AIC criteria．