Pseudoknots are RNA tertiary structures which perform essential biological functions. This paper discusses SARNA-Predict-pk, a RNA pseudoknotted secondary structure prediction algorithm based on Simulated Annealing (SA). The research presented here extends previous work of SARNA-Predict and further examines the effect of the new algorithm to include prediction of RNA secondary structure with pseudoknots. An evaluation of the performance of SARNA-Predict-pk in terms of prediction accuracy is made via comparison with several state-of-the-art prediction algorithms using 20 individual known structures from seven RNA classes. We measured the sensitivity and specificity of nine prediction algorithms. Three of these are dynamic programming algorithms: Pseudoknot (pknotsRE), NUPACK, and pknotsRG-mfe. One is using the statistical clustering approach: Sfold and the other five are heuristic algorithms: SARNA-Predict-pk, ILM, STAR, IPknot and HotKnots algorithms. The results presented in this paper demonstrate that SARNA-Predict-pk can out-perform other state-of-the-art algorithms in terms of prediction accuracy. This supports the use of the proposed method on pseudoknotted RNA secondary structure prediction of other known structures.