Accurate reconstruction of phylogenetic trees often involves solving hard optimisation problems, particularly the Maximum Parsimony (MP) and Maximum Likelihood (ML) problems. Various heuristics yield good results for these problems within reasonable time only on small datasets. This is a major impediment for large-scale phylogeny reconstruction. Roshan et al. introduced Rec-I-DCM3, an efficient and accurate meta-method for solving the MP problem on large datasets of up to 14,000 taxa. We improve the performance of Rec-I-DCM3 via parallelisation. The experiments demonstrate that our parallel method, PRec-I-DCM3, achieves significant improvements, both in speed and accuracy, over its sequential counterpart.