The purpose of this study is to formulate an Analytical model of equispaced energy levels quantum wells (QWs) in semiconductor ternary alloys (AxB1-xC). The procedure is by mapping the envelop function Schrodinger equation for realistic QW, with the local conduction band edge as the potential experienced by an electron in the QW into an effective mass Schrodinger equation with a linear harmonic oscillator potential by the method of coordinate transformation. The electron effective mass and potential are then obtained as the signature for the equispaced energy level for QWs in semiconductor ternary alloys.