Molecular structure optimization plays an important role in computational chemistry and materials science. This study presents a genetic algorithm-based approach to optimize the 3-D molecular structure of a carbon chain by minimizing its Lennard-Jones potential energy. The algorithm begins by generating a random initial population of valid molecular structures. Through iterative selection, crossover, and mutation, new molecular structures are generated and evaluated using the Lennard-Jones potential to estimate their stability. This approach demonstrates an efficient computational framework for generating stable molecular configurations faster and accurately, which can be extended to more complex organic molecules.