We present a non-linear simulation of the three-dimensional fingering dynamics of the miscible fingering phenomenon in the Hele-Shaw cell, which is tapered in the direction of fluid displacement. The flow displacement is governed by the continuity equation, Darcy’s equation, and the convection-diffusion equation. Moreover, the consequences of dispersion induced by flow at the pore scale are disregarded. A finite element method-based approach is used to perform the non-linear simulations. It is observed that the existence of a depth gradient can modify the stability of the interface, providing possibilities to alter fingering instabilities. The role of fluid rheology in the transient evolution of concentration fields and fingering patterns defined using quantities such as average concentration profiles, relative contact area, finger width, and breakthrough time are investigated. It is observed that the sweeping efficiency is enhanced in the converging tapered cells. Overall, the stability of the interface is characterized by the interaction between the viscosity contrast and the depth variation of the Hele-Shaw cell. The research may prove useful in the development of a small-taper Hele-Shaw cell that facilitates methodical management of fingering instabilities.