The dissolution-induced finger pattern in geological medium plays an important role in both geological processes and engineering practices. Numerical models have been developed to investigate the evolution of the chemical dissolution front within a fluid-saturated porous medium. In these models, several permeability-porosity relationships have been proposed and incorporated into the numerical model for describing simultaneous changes in permeability and porosity induced by mineral dissolution, but limited experimental data are available to justify one form superior to the other. This study investigates the effects of the permeability-porosity relationships on the morphological evolution of the chemical dissolution front. Three porosity-permeability relationships, namely, modified Fair-Hatch, Kozeny-Carman and Verma-Pruess (VP) models are incorporated into the numerical model. A series of numerical simulations are performed to evaluate the morphological evolution of reaction front, and the corresponding behaviour diagrams are constructed. Results shows that the morphological development are similar each other for modified Fair-Fatch and Kozeny-Carman model. The VP model yields a relative low primary and secondary critical upstream pressure gradient value owing to the flow-focusing effect enhanced by the stronger dependence of permeability on porosity. A comparison of behaviour diagrams of front morphology among three relationships show that the double-fingering front occurs under condition of lower upstream pressure gradient and smaller non-uniformity spacing for VP model. Our simulations demonstrate that the choice of the permeability-porosity function plays important roles on the evolution patterns of dissolution front. Therefore, an adequate description of the permeability-porosity relationship may lead to a more realistic simulation of field problems.