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In most of the successful real protein structure prediction (PSP) problem, lattice models have been essentially utilized to have the folding backbone sampling at the top of the hierarchical approach. A three dimensional face-centred-cube (FCC), with the provision for providing the most compact core, can map closest to the folded protein in reality. Hence, our successful hybrid genetic algorithms (HGA) proposed earlier for a square and cube lattice model is being extended in this paper for a 3D FCC model. Furthermore, twins (conformations having similarity with each other), in GA population have also been considered for removal from the search space for improving the effectiveness of GA The HGA combined with the twin removal (TR) strategy showed best performance when compared with the simple GA (SGA), SGA with TR, and HGA only versions. Experiments were carried out on the publicly available benchmark HP sequences and results are expressed based on the fitness of the corresponding applied lattice model, which will help any future novel approach to be compared.