This paper presents a statistical approach to predict the behavior of liftoff grains on the basis of simulation of random collisions between incident grains and the mixed sand bed by means of the particle dynamics method (PDM). In the simulation a two-dimensional sand bed of grain-grain contact between the mixed size grains, which are simplified by circular disks, is stochastically generated by a random number generator and the "particle cooling" technique. After the diameter distribution of incident grains is divided into n subregions of representative diameters, first, the collisions are simulated for each representative diameter of incident grains with an incident velocity impacting the mixed sand bed, for which the information about liftoff grains may be gained at the end of collisions. After that a statistic approach is proposed to get the average values of velocity and number of the ejecting and rebounding grains as well as the probability density function (pdf) of liftoff velocity in terms of magnitude and angle. In order to guarantee steady state of the statistical quantities, 110 samples of the random collisions of each representative diameter of grains with an incident velocity but different (or random) contact position are taken in a case study in which the average diameter of the grains is the same as that of the uniform sand grains employed by Anderson and Haff (1991). The numerical results show that there are notable differences in the statistical quantities between them, and some of the results obtained here are in good agreement with the measurement data of multiple grain size. Finally, the pdf of initial velocity in terms of both magnitude and angle is derived on the basis of the simulation results.