In this paper, we propose a distributionally robust model for a (0-1) stochastic quadratic bi-level programming problem. To this purpose, we first transform the stochastic bi-level problem into an equivalent deterministic formulation. Then, we use this formulation to derive a bi-level distributionally robust model (Liao, 2011). The latter is accomplished while taking into account the set of all possible distributions for the input random parameters. Finally, we transform both, the deterministic and the distributionally robust models into single level optimization problems (Audet et al., 1997). This allows comparing the optimal solutions of the proposed models. Our preliminary numerical results indicate that slight conservative solutions can be obtained when the number of binary variables in the upper level problem is larger than the number of variables in the follower.