By means of the Hermitian metric and Chern connection, Qiu [4] obtained the Koppelman--Leray--Norguet formula for (p,q) differential forms on an open set with C¹ piecewise smooth boundary on a Stein manifold, and under suitable conditions gave the solutions of \overline{\partial}-equation on a Stein manifold. In this article, using the method of Range and Siu [5], under suitable conditions, the authors complicatedly calculate to give the uniform estimates of solutions of \overline{\partial}-equation for (p,q) differential forms on a Stein manifold.