In this paper we have synthesized optimal control of multi-level quantum system by representing unitary operator in terms of the projection operators of the Hamiltonian of the system. We have solved the steering problem for multi-level quantum systems minimizing energy cost functional of the control. The optimal control problem of the time evolution of quantum spin of Pauli two-level system subjected to an external field with the minimum energy function is also illustrated and formulated in terms of the quantum spin up and spin down states of the Pauli two-level system.