The complexity of most biomedical/bioinformatics problems requires efficient solutions using collaborative/parallel computing. One promising solution is to implement Grid computing, as an emerging new field called BioGrid. However, one of the most stringent requirements in such a Grid-based solution is data privacy. This paper presents a novel solution to provide the Confidentiality when using the Grid to efficiently solve MISD biomedical problems. It is called the Grid-Based Pseudo-Cache (GBPC) solution. It is proved to have equal or better performance than traditional MIMD solution. Via case studies our theories are validated in practice, and the data dependence is also addressed.