Mixed integer linear programs (MILP) are flexible and powerful tool for modeling and solving many difficult real-world combinatorial optimization problems. In this paper, we propose a novel machine learning-based framework ConPaS that learns to predict solutions to MILPs with contrastive learning. For training, we collect high-quality solutions as positive samples and low-quality or infeasible solutions as negative samples. We then learn to make discriminative predictions by contrasting the positive and negative samples. During test time, we predict assignments for a subset of integer variables of a MILP and then solve the resulting reduced MILP to construct high-quality solutions. Empirically, we show that ConPaS achieves state-of-the-art results compared to other ML-based approaches in terms of the quality of and the speed at which the solutions are found.