In this paper, we investigate intuitionistic fuzzy Poisson equation with uncertain parameters, considering the parameters as intuitionistic fuzzy numbers. We apply a finite difference method to solve ’Intuitionistic fuzzy Poisson equation’. The continuity of the membership and non-membership functions (which imply the continuity of the hesitancy function) is used to obtain qualitative properties on regular α-cut and β-cut of the intuitionistic fuzzy solution. The fuzzification of the deterministic α-cut and β-cut solutions obtained lead to the intuitionistic fuzzy solution. Finally, an example is presented to illustrate the proposed methodology as well as to show a graphical representation of its corresponding intuitionistic fuzzy solution.