This research investigates the problem of synchronous vibrations suppression in an active magnetic bearing (AMB) system without a rotating speed sensor. The mass imbalance of the rotor is intractable in the AMB system, which will substantially compromise the stability and safety of the system during operation. To realize the unbalance control, rotating speed sensors are commonly employed to gauge the rotating speed. However, the rotating speed sensors cannot operate routinely in special environments. This work proposes an adaptive period iteration control (APIC) algorithm combined with a three-module real-time rotating speed estimator (TMRRSE) to address the above problems. The TMRRSE uses the positions of the rotor at different moments to calculate the rotating speed. And it can also adjust the anti-noise performance and precision by its parameters and has significant tracking performance. The APIC algorithm can adaptively suppress the current vibrations based on the period iteration strategy. In addition, the stability of the overall control scheme is demonstrated using the Lyapunov method. Finally, simulation and experimental results demonstrate the effectiveness of the overall control scheme.