This paper presents a new Genetic Algorithm for Protein Structure Prediction problem in both 2D and 3D hydrophobichydrophilic lattice models, introduced in [1]. Our algorithm evolves a new local-search genetic operation (called Pull-Move and well described in [2]), into the standard GA1 ([3,4]). The experiments show that performing a set of Pull-Moves in addition to standard genetic operations in GA (such as crossover and mutation) leads to significant energy improvements. The paper also introduces the Global Energy as fitness function and explains the advantages of utilizing it rather than the standard Free Energy. The experimental results are even more impressive when using the Global Energy as fitness function in GA. ACM Categories and Subject Descriptors I.2.8 [Artificial Intelligence]: Problem Solving, Control Methods and Search General Terms: Algorithms, Experimentation