Transport property prediction of fatty acid methyl esters (FAMEs) is essential to its utilisation as biodiesel and biolubricant which can work under high-pressure conditions. Equilibrium molecular simulation is performed to study the viscosity, diffusivity, density and molecular structure dynamics at conditions up to 300 MPa. Among the transport properties, convergence of the viscosity needs a sufficiently large number of independent replications of the simulation. The system size effect on diffusion coefficient should be taken into consideration in fitting the Stokes-Einstein relation. The capability of three different force fields on predicting transport properties is evaluated in terms of the united-atom molecular model and all-atom molecular model. The solidification of FAMEs under high pressure occurs with parallel molecular alignment. The spatial inhomogeneity results in the breakdown of Stokes-Einstein relation. A hybrid effective hydrodynamic radius is established on the linear relation between experimental viscosity and diffusion coefficient in molecular simulation. This provides a predictive method to estimate viscosity from molecular diffusion coefficient over a broad range of conditions provided that Stokes-Einstein relation applies. Peer Reviewed