We consider a single-Cooper-pair box biased by a classical voltage and also irradiated by a single-mode quantized field. We investigate the dynamical behavior of the Pancharatnam phase and the geometric phase of the system,and find that the dynamic behavior of the Pancharatnam phase decreases with time,and the geometric phase increases with time. When the decreasing rate of Pancharatnam phase is large,the increasing rate of geometric phase is small,and vice versa.