This paper proposes a Particle Swarm Optimization (PSO) algorithm called HelixPSO for finding RNA secondary structures that have a low energy and are similar to the native structure. HelixPSO is compared to the recent algorithms RnaPredict, SARNA-Predict, SetPSO, and RNAfold. For a set of standard RNA test sequences it is shown that HelixPSO obtains a better average sensitivity than SARNA-Predict and SetPSO and is as good as RNA-Predict and RNAfold. When best values for different measures (e.g., number of correctly predicted base pairs, false positives, and sensitivity) over several runs are compared, HelixPSO performs better than RNAfold, similar to RNA-Predict, and is outperformed by SARNA-Predict. It is shown that HelixPSO complements Rna-Predict and SARNA-Predict well since the algorithms show often very different behavior on the same sequence. Furthermore, a parallel version of the HelixPSO is proposed and it is shown that good speedup values can be obtained for small to medium size PC clusters.