The problem of mass/heat transfer from a viscous droplet is solved by using a finite-difference scheme. and a dual kind of computational grid. The steady-state Navier-Stokes and energy equations for the flow fields inside and outside a viscous sphere in a fluid of different properties are fully solved numerically for Reynolds numbers (Re) ranging from 1 to 500. The corresponding Peclet numbers (Fe) range from 1 to 1000. At high values of Re and Pe a thermal and a momentum boundary layer are formed in the outside fluid. For this reason, we adopted a method of a two sub-layer concept for the computational domain outside the sphere. The first of these computational sub-layers is positioned at the interface of the sphere and covers a thin region [of O(Re-1/2) for the momentum and of O(Pe(-1/2)) for the thermal boundary layer]. The second computational layer is based on an exponential function and covers the rest of the domain. We utilize this numerical technique to compute the Nusselt numbers for viscous spheres at different values of Re, Pe and the viscosity ratio. The computations also show that the effect of the internal fluid density on the heat or mass transfer is negligible.