This paper proposes an algorithm to compute the optimal switching cost from the dynamic programming Hamilton-Jacobi-Bellman (HJB) equations. For the optimal switching control problem, the HJB equation is a System of Quasi-Variational Inequalities (SQVIs) coupled by a nonlinear operator. By exploring the fundamental limit on the number of switches could occur in an optimal switching control signal and making use of the connections with the optimal stopping control problem, the coupled SQVIs are decoupled into a sequence of optimal stopping type Quasi-Variational Inequalities (QVIs). The optimal stopping QVIs are solved by the approach of Markov chain approximation.