Abstarct: In this thesis, Methods we of Power Factor Correction (PFC) in single-phase full-wave rectifier to examine. Since we are looking for a place with minimum ripple voltage, we use capasitors with high-capacity. Because of Its sim simplicity and inexpensivity. Not only then high-capasitity capacitors smooth the output voltage, but also reduce diode conduction time. The diode conduction time reduction cause the phase diffrence between current non-sinusidalinput voltage and input current. This two problems cause reduce power factor and increace total harmonic distotion (THD). At first, the power factor improvement is checked by a passive method and the we analyze the power factor improvement by active method. In this method, first we consider the power factor improvement at low frequency then this method analyzed by both continues and discontinues mode using high frequency. At the end we want to design controller using sliding mode control to ply to rules: first, the power factor correction in boost converter at continues mode and adjust output voltage to value greater than input voltage reference.