Multiclass classification is an important technique to many complex biomedicine problems. Genetic algorithms (GA) are proven to be effective to select features prior to multiclass classification by support vector machines (SVM). However, their use is computation intensive. Based on SOA (Service Oriented Architecture) design principles, this paper proposes a cloud computing framework that exploits the inherent parallelism of GA-SVM classification to speed up the work. The performance evaluations on an mRNA benchmark cancer dataset have shown the effectiveness and efficiency of the framework. With a user-friendly web interface, the framework provides researchers an easy way to investigate the unrevealed secrets in the fast-growing repository of biomedical data.