This work deals with modelling and numerical simulation of complete evaporation process inside anisotropic porous media. Based on the modified enthalpy formulation of Two-Phase Mixture Model (TPMM) along with the assumption of Local Thermal Non-Equilibrium (LTNE), a modified formulation has been proposed that can easily accommodate the anisotropy in the porous media properties. The governing equations have been solved using the Finite Volume Method (FVM) on staggered grid layout. The simulations have been carried out by applying the proposed smoothing algorithm for the effective diffusion coefficient in order to avoid the non-physical jump in the predicted temperature distribution during the numerical simulations. The effects of the permeability ratio, solid thermal conductivity ratio, thermal conductivity of the solid phase and the Darcy number have been investigated. The computed results show that the anisotropy of permeability and thermal conductivity of the solid phase have significant effect on the initiation and termination of phase change process. It is also observed that the anisotropic properties of the porous medium have significant influence on the flow behaviour and heat transfer rate from that expected under isotropic conditions. The results indicated that the effect of thermal conductivity of the solid phase plays an important role and hence adequate care must be taken while designing such evaporators. The results also show that the smoothing algorithm is successful in dealing with the rapid change in the effective diffusion coefficient during the simulations of complete evaporation process.