We present a theoretical study of an optical cavity coupled with single four-level atoms in closed loop formed via applied control lasers.The transmitted probe field from the cavity is analyzed.We show that the electromagnetically induced transparency (EIT) in the cavity and the normal mode splitting will be very different with changing the closed interaction phase and the intensity of the free-space control laser.This coupled cavity-atom system presents a variational double-EIT that comes from modulating the splitting of the dark state,which means that we could realize the gradual transfer between one EIT peak and two EIT peaks by adjusting the applied control lasers,and the normal mode splitting sidebands will shift slightly by changing the free-space control laser.This means that we could control the output cavity probe field more freely and it is easer to realize optical switch controlled by more parameters.We also depict the angular dispersion of the intracavity probe field in different free-space control laser.The large phase shift (-π → π) of the reflected intracavity probe field will be very useful for optical temporal differentiation and quantum phase gate.