In order to provide advice on the control of the geometric phase of a quantum system

it explores the Berry phase in a tunneling double-quantum-dot molecule interacting with a quantized single-mode field by the full quantum theory. Effects of parameters

such as the mean photon number of the field

field-dot detuning

tunneling energy-level detuning

linear and nonlinear field-dot coupling

on the geometric phase were researched. The results show that in the region where anticrossing of the eigenenengy levels of the system occurs

the Berry phase can be efficiently controlled by adjusting the applied voltage exerted on the quantum-dot molecule. The conclusion may be applied in quantum computation.