Summary: ``Coupled dispersionless (CD) equation is an important integrable model since it describes the current-fed string in a certain external magnetic field. Recently, Ablowitz and Musslimani introduced a class of reverse space, reverse time and reverse space and time nonlocal integrable equations, including nonlocal nonlinear Schrödinger equation, nonlocal sine-Gordon equation and nonlocal Davey-Stewartson equation etc. In this paper we study an integrable reverse space and time nonlocal CD equation. By applying the Darboux transformation, we present the one-soliton and two-soliton solutions for the nonlocal CD equation. We also show the asymptotic analysis of the one-soliton solution from nonzero seed and two-soliton solutions.''