Improving the accuracy and efficiency of computational RNA secondary structure prediction is an important challenge, particularly for pseudoknotted secondary structures. We propose a new approach for prediction of pseudoknotted structures, motivated by the hypothesis that RNA structures fold hierarchically, with pseudoknot free pairs forming initially, and pseudoknots forming later so as to minimize energy relative to the initial pseudoknot free structure. Our HFold (Hierarchical Fold) algorithm has O(n ³) running time, and can handle a wide range of biological structures, including nested kissing hairpins, which have previously required Θ(n ⁶) time using traditional minimum free energy approaches. We also report on an experimental evaluation of HFold.