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Three dimensional structure prediction of a protein from its amino acid sequence, known as protein folding, is one of the most studied computational problem in bioinformatics and computational biology. Since, this is a hard problem, a number of simplified models have been proposed in literature to capture the essential properties of this problem. In this paper we introduce the hexagonal lattices with diagonals to handle the protein folding problem considering the well researched HP model. We give two approximation algorithms for protein folding on this lattice. Our first algorithm is a 5/3 -approximation algorithm, which is based on the strategy of partitioning the entire protein sequence into two pieces. Our next algorithm is also based on partitioning approaches and improves upon the first algorithm. [ABSTRACT FROM AUTHOR]