The study on the determination of ground state energy of exotic muonic helium system by variational principle approximation has been done. The basic ideas of this method are to choose a trial wave function consisting of an adjustable variational parameter and to minimize the expectation value of its Hamiltonian operator which is called the average energy. The trial wave function used is the ground state hydrogenic ion wave function (orbital approximation). The operator Hamiltonian of this system is operated on the trial wave function and its value is minimized, from which the ground state energy of this system was found to be about . This value is greater than that of both atom and system . This difference is caused by the difference in the reduced masses of these systems in the orbital approximation. Keywords: Hydrogenic ions, Ground state energy, Trial wave function, Orbital approximation, Variational Principle.