We propose a method of controlling the dc-SQUID (superconducting quantum interference device) systemby changing the gate voltages, which controls the amplitude of the fictitious magnetic fields Bz, and the externallyapplied current that produces the piercing magnetic fiux φx for the dc-SQUID system. We have also introduced aphysical model for the dc-SQUID system. Using this physical model, one can obtain the non-adiabatic geometric phasegate for the single qubit and the non-adiabatic conditional geometric phase gate (controlled NOT gate) for the twoqubits. It is shown that when the gate voltage and the externally applied current of the dc-SQUID system satisfies anappropriate constraint condition, the charge state evolution can be controlled exactly on a dynamic phase free path. Thenon-adiabatic evolution of the charge states is given as well.