Virtual Cluster (VC) migration is needed in Cloud Computing (CC) during situations like load balancing, fault tolerance ,complying with Service Level Agreement(SLA) etc. While migrating VC from one Physical Machine(PM) to another PM various constraints are considered for an optimal solution. The proposed Backtracking algorithm which has provided optimal solutions for popular problems like NQueens, Hamiltonian cycle, selects a set of VMs in a VC to be migrated on satisfying the criteria of the provider such as minimum total migration time, little/minimum down time better power management and increase in performance etc.