In this paper, deformation of viscoelastic drop in a microscale flow with sudden constriction is studied numerically. . The effect of polymeric viscosity on deformation of viscoelastic fluid is studied for two different solvent viscosity ratio and two different channel confinement in two-phase viscoelastic drop-Newtonian matrix system. The Finitely Extensible Non-linear Elastic–Peterlin (FENE-P) model was used to model the viscoelastic drop. The simulation was performed using open source solver Basilisk. The viscoelastic drop with lower polymeric viscosity and higher solvent viscosity seemed to undergo appreciable deformation inside constricted microchannel when subjected to sudden contraction. The low polymeric viscosity of a viscoelastic fluid corresponds to a dilute polymeric solution, its viscoelastic behavior is best explained by seeing its deformation under high shear flows inside microchannel. The isolated arrangement of polymeric coils in dilute polymeric solutions assists independent molecular movement, which supports their deformation under high shear flows. The FENE-P drop model used in the present study, at higher solvent viscosity, exhibit faster stress relaxation and remarkable elastic recovery in the expansion zone of the microchannel. The dilute FENE-P viscoelastic fluid can also be considered as a significant model to predict the viscoelastic behavior of useful polymeric fluids like hydrogels, paints, and vesicles, etc.