This paper presents a Hybrid Genetic Algorithm (HGA) for the protein folding prediction (PFP) applications using the 2D face-centred-cube (FCC) Hydrophobic-Hydrophilic (HP) lattice model. This approach enhances the optimal core formation concept and develops effective and efficient strategies to implement generalized short pull moves to embed highly probable short motifs or building blocks and hence forms the hybridized GA for FCC model. Building blocks containing Hydrophobic (H) - Hydrophilic (P or Polar) covalent bonds are utilized such a way as to help form a core that maximizes the |fitness|. The HGA helps overcome the ineffective crossover and mutation operations that traditionally lead to the stuck condition, especially when the core becomes compact. PFP has been strategically translated into a multi-objective optimization problem and implemented using a swing function, with the HGA providing improved performance in the 2D FCC model compared with the Simple GA.