This paper presents a rotordynamic analysis and experimental characterization of a novel concept of a controllable gas foil bearing (C-GFB) with piezoelectric (PZT) actuators. The C-GFB consists of bump foil structures and three PZT actuators, and the PZT actuators push the bump foil structures in different displacements according to the driving voltage, enabling preload control. In order to predict the piezoelectric preload according to the driving voltage, an equivalent spring model for PZT actuators and foil structures is introduced. In addition, PZT parameters (a piezoelectric constant and stiffness) are measured through parameter identification tests using a latch. Next, static lubrication analysis for C-GFB reveals that the gas-film pressure reduces the effect of piezoelectric preload by up to a maximum of 11%, because the piezoelectric actuator has structural compliance so that it is structurally deformed by the pressure. Finally, nonlinear orbit simulation is performed, and the performance of real-time vibration control of C-GFB is evaluated. The real-time preload control is carried out at ~32.6 krpm, where the rotordynamic instability sufficiently occurs. As the driving voltage increases, the instability suppression and delay effect increase. In particular, when controlled at 150 V, the onset speed of the instability increases to 79.1 krpm. Consequently, this study demonstrates that the GFB with piezoelectric preloads is a simple, effective, and real-time method to improve the rotordynamic stability.