This paper presents a novel approach to control a boost PFC AC/DC converter without using any current sensors. Due to the particular structure of the boost PFC AC/DC converter, sensorless control of the converter is very challenging. As illustrated in this paper, the converter loses its observability for some operating points. This is the reason that the sensorless control of the boost PFC entails special attentions. A very simple and practical senseless scheme is proposed in this paper, which is able to accurately estimate the inductor current for the entire operating range of the converter. In addition, a very simple and practical closed-loop control approach is proposed in order to improve the transient response of the single-phase boost PFC converter. This approach eliminates the need for filtering double frequency ripple from the output voltage, which allows increasing the bandwidth of the external voltage loop. Simulation and experimental results validate the feasibility of the proposed technique and confirm its superior performance compared to the conventional control system.