The power factor correction (PFC) converters built for telecom applications must meet certain standards in order to keep the total harmonics distortion (THD) at the specified low levels to reduce the current stresses, reduce the power losses and hence increase the converter efficiency and input power factor (PF). Thus, in this paper, the small-signal stability models of the telecom bridge and bridgeless PFC converters are derived and based on the derived stability models, the fast-dynamic response integral-proportional (IP) current control technique is proposed to improve the control loops performance around the current waveform zero-crossing point, reduce zero crossing distortion (ZCD), reduce the THD, and reaches the input current PF near to unity. The digital simulation modeling using PSIM software of the 2.5 kW bridge and bridgeless PFC converters is performed to show the converter's performance with the proposed current technique as compared with the conventional proportional-integral (PI) control technique. The proposed current controller in this work improves the current control loop performance, reduces the ZCD period, reduces the THD to about 5% and reaching converters input PF near unity in both bridge and bridgeless PFC converters.