Hyperbolic conservation equations for polydisperse, high-speed, compressible, fluid–particle flows with added mass and fluid-phase pseudoturbulence are derived. First, the kinetic-based model for monodisperse particles that accounts for collisional and frictional pressure, as well as added mass and internal energy, is reviewed. Then, a kinetic-based model for polydisperse particles is formulated in terms of the moments of the particle size distribution, and velocity moments conditioned on the particle mass or size. Transport equations for velocity moments up to second order (or total kinetic energy) are closed using the hyperbolic quadrature method of moments. In the numerical implementation for the spatial fluxes and source terms, the particle mass distribution is treated using the generalized quadrature method of moments and the size-conditioned moments are found with the conditional quadrature method of moments. Example results for spatially 1-D test cases demonstrate the ability of the polydisperse model to capture a wide range of particle-size-dependent multiphase flow physics.