Various processor architectures have been proposed until today, and the performance has improved remarkably. Recently, the Chip Multi-processors (CMPs), which has many processor cores onto a chip, are proposed for further performance improvement. The Cell processor is one of such CMP and shows high computational performance. Although this processor is designed for the multimedia, that high performance character can be utilized to molecular orbital calculation. In this study we implemented Fock matrix construction program on the Cell processor, and evaluated computational performance. As a result, there were two kinds of main stalls by the branch prediction and the data alignment, which are controlled by software mechanism for the simplification of the Cell processor hardware. It is possible to improve the performance about 30%, if the branch prediction hit ratio could be improved to 99%. For data alignment stall, a part of stalls, which is originated by data shuffle pipeline, could be decreased by preparing hardware data alignment mechanism.