Turbulent premixed flame propagation in a closed spherical vessel with a homogeneous and isotropic turbulent flow field is modelled using the one-point transport equation for the probability density function (pdf) in the thermodynamic space. The pdf equation is discretized using the control volume formulation on a one-dimensional spherical grid. Then the discretized equation is solved using the Monte Carlo method to follow particles with variable volumes on a grid moving with the expansion radial velocity. The mixing term is modelled using the Curl model, and the modified Curl model. The source term is simulated deterministically using a one-step chemical reaction mechanism. Transient solutions are obtained for spherical benzene-air flames using frozen turbulent flow. The pressure rise, the mass fraction burned, the flame speed, the entrainment speed, the burning speed, and the burned gas speed are calculated. The calculated entrainment speeds are compared with the ones reported in Bradley et al (1992) for KLe>5.3 where distributed reaction zones are assumed to govern the flame propagation. The effects of different turbulent flow field (u'/S-1) and the effect of the product (KLe) are discussed.