RNA-RNA interactions play fundamental roles in gene and cell regulation. Therefore, accurate prediction of RNA-RNA interactions is critical to determine their complex structures and understand the molecular mechanism of the interactions. Here, we have developed a physics-based double-iterative strategy to determine the effective potentials for RNA-RNA interactions based on a training set of 97 diverse RNA-RNA complexes. The double-iterative strategy circumvented the reference state problem in knowledge-based scoring functions by updating the potentials through iteration and also overcame the decoy-dependent limitation in previous iterative methods by constructing the decoys iteratively. The derived scoring function, which is referred to as DITScoreRR, was evaluated on an RNA-RNA docking benchmark of 60 test cases and compared with three other scoring functions. It was shown that for bound docking, our scoring function DITScoreRR obtained the excellent success rates of 90% and 98.3% in binding mode predictions when the top 1 and 10 predictions were considered, compared to 63.3% and 71.7% for van der Waals interactions, 45.0% and 65.0% for ITScorePP, and 11.7% and 26.7% for ZDOCK 2.1, respectively. For unbound docking, DITScoreRR achieved the good success rates of 53.3% and 71.7% in binding mode predictions when the top 1 and 10 predictions were considered, compared to 13.3% and 28.3% for van der Waals interactions, 11.7% and 26.7% for our ITScorePP, and 3.3% and 6.7% for ZDOCK 2.1, respectively. DITScoreRR also performed significantly better in ranking decoys and obtained significantly higher score-RMSD correlations than the other three scoring functions. DITScoreRR will be of great value for the prediction and design of RNA structures and RNA-RNA complexes.