Abstract: Pressure swirling atomizers are wildly used in the fuel injection systems of aero-engines, marine engines, vehicle gasoline direct injection engines and gas turbines, et al. Considering about a pressure swirling atomizer liquid jet, the correlation of breakup droplet size and velocity distributions of an annular swirling viscous liquid sheet is studied. Joint probability density function of droplet size and velocity distribution of an annular swirling viscous liquid sheet is reduced based on maximum entropy method. The correlation between droplet size distribution and droplet velocity distribution are then discussed. Results show that with the right form of joint probability density function, the conservation laws of mass, momentum and energy must be included together as the constraint conditions. Droplet size and velocity distributions are closely related. And the liquid sheet swirling strength does not affect the structure of joint probability density function a lot, but the liquid swirling strength affect the distribution region to some extent.