Distance correlation is a relatively new measure of dependence in probability theory and statistics, which has the great advantage that it gives zero if and only if the variables are independent. In this paper we define its possibilistic version. Namely, we equip each γ -level set of the joint possibility distribution with a uniform probability distribution, then we determine the probabilistic distance covariance and correlation between the marginal distributions. Finally, the possibilistic distance covariance and correlation is computed as the weighted average of these probabilistic measures of dependence.