Proteins are complex structures made of amino acids having a fundamental role in the correct functioning of living cells. The structure of a protein is the result of the protein folding process. However, the general principles that govern the folding of natural proteins into a native structure are unknown. The problem of predicting a protein structure with minimum-energy starting from the unfolded amino acid sequence is a highly complex and important task in molecular and computational biology. Protein structure prediction has important applications in fields such as drug design and disease prediction. The protein structure prediction problem is NP-hard even in simplified lattice protein models. An evolutionary model based on hill-climbing genetic operators is proposed for protein structure prediction in the hydrophobic - polar (HP) model. Problem-specific search operators are implemented and applied using a steepest-ascent hill-climbing approach. Furthermore, the proposed model enforces an explicit diversification stage during the evolution in order to avoid local optimum. The main features of the resulting evolutionary algorithm - hill-climbing mechanism and diversification strategy - are evaluated in a set of numerical experiments for the protein structure prediction problem to assess their impact to the efficiency of the search process. Furthermore, the emerging consolidated model is compared to relevant algorithms from the literature for a set of difficult bidimensional instances from lattice protein models. The results obtained by the proposed algorithm are promising and competitive with those of related methods.