Generalized Heun-type differential equation appears in the study of quantum systems, particularly in the calculation of energy levels and wave functions. A particular case of generalized Heun type differential equation is solved using a special approach called tridiagonal representation approach. The differential equation has five singularities: four regular and one irregular at infinity. The differential equation is solved in terms of Jacobi polynomials in a series. This series’ expansion coefficients fulfill a three-term recurrence relation, so forming a new class of orthogonal polynomials.