Classical orthogonal polynomials of a discrete variable on non-uniform lattices were introduced by \textit{R. Askey} and \textit{J. A. Wilson} [SIAM J. Math. Anal. 10, 1008-1016 (1979; Zbl 0437.33014)], and \textit{J. A. Wilson} [ibid. 11, 690-701 (1980; Zbl 0454.33007)] and their main properties were established on the basis of the theory of hypergeometric and basic hypergeometric series. In this paper, the authors study the fundamental properties of the Askey-Wilson polynomials on the basis of a generalization of \textit{W. Hahn's} approach [Math. Nachr., Berlin 2, 4-34 (1949; Zbl 0031.39001)] and obtain basic hypergeometric forms of hypergeometric type difference equation, Rodrigues type formula, series expansion, difference differentiation formula, orthogonality property and of the property of moments for the polynomial solutions of hypergeometric type difference equation.