This paper proposes a zeroth-order adaptive momentum method for black-box optimization, by approximating the stochastic gradient using the forward difference of two function values at a random unit direction. The paper also shows the convergence analysis in terms of Mahalanobis distance for both unconstrained and constrained nonconvex optimization with the ZO-AdaMM, which results in sublinear convergence rates that are roughly a factor of the square root of dimension worse than that of the first-order ZO-AdaMM, as well as for constrained convex optimization. The proposed scheme is quite interesting, which solves the (non)convex optimization in a new perspective, and somewhat provides new insight to the adaptive momentum methods. In particular, the paper provides a formal conclusion that the Euclidean projection may results in non-convergence issue in stochastic optimization. The paper also shows the applications to black-box adversarial attacks problems and validate the method by comparing it with other ZO methods.