The A_n type cluster variety, denoted by X_n, is the affine scheme associated to the upper cluster algebra of the A_n quiver (of n unfrozen vertices and one frozen vertex). The dual of X_n is denoted as Y_n, and is isomorphic but not canonically to X_n. For example, the variety X_1 is given by the equation {x y = 1 + q} where x, y are in \C and q is in \C^*. We prove that the homological mirror symmetry (HMS) conjecture for X_n, Y_n: the coherent sheaf category of Coh(X_n) is equivalent to the wrapped Fukaya category WFuk(Y_n), generalizing the known case for n=1 and 2. This is based on a recent work of Gammage-Le on HMS for truncated cluster variety, by putting back the 'truncated' part. This is work in progress, and is joint with Linhui Shen and Zhe Sun.