The eigenvalue problem in a non-concentric circular quantum corral was studied with a conformal mapping method. The energy spectra of electrons show the properties of anti-crossing between the nearby energy levels. This property of energy spectra is caused by the Jacobian of the conformal transformation. We also give the probability density of the electronic states that confined in the non-concentric circular quantum corral. Quantum corral geometry has a stronger effect on electronic states of higher energies than that of lower energies.