The liftoff angular velocities, including the rebound ones and the ejected ones, of sand particles in a windblown sand flux have a significant influence on the saltation trajectories and the transport flux and so on. However, they are not easy to determine actually both in field and in a wind tunnel, especially when the sand particles are small and the wind speed is low. A stochastic particle-bed collision model is developed in this paper to calculate the liftoff angular velocities. Having taken the incident velocity and angle of an incident particle, the impact angle between the incident and the impacted particles in the sand bed and its creep velocity as well as the contact angle between the impacted particle and other particles in the bed as random variables in the collision model, the probability distributions of the liftoff angular velocities for different particle diameters and wind speeds are gained and agree well to the experimental results. The rebound probability distribution function looks like Gumbel distribution with a cusp in the peak, and the ejected one looks like the normal one. The effect of the wind speed and the particle diameter on the probability density functions is discussed in detail.