In this paper, we focus on the combination of probabilistic logic programming with the principle of maximum entropy. We start by defining probabilistic queries to probabilistic logic programs and their answer substitutions under maximum entropy. We then present an efficient linear programming characterization for the problem of deciding whether a probabilistic logic program is satisfiable. Finally, and as a main result of this paper, we introduce an efficient technique for approximative probabilistic logic programming under maximum entropy. This technique reduces the original entropy maximization task to solving a modified and relatively small optimization problem.