This paper concerns the solution for a kind of non-homogeneous recurrence of variable coefficients with two indices. G. Tu [Chin. Ann. Math. 2, 431-436 (1981; Zbl 0477.10014)] considered the homogeneous and constant coefficients case in 1981. In this paper, Tu’s formula is extended. A formula for the solution of the non-homogeneous recurrence with variable coefficients is then presented.