A frequency synthesizer enabling fine setting of frequency in a wide band according to a new principle and having a wide frequency acquisition range. By using specific solving means, the sinusoidal signal of output frequency of a voltage-controlled oscillating section is subjected to quadrature detection, a vector rotating at a frequency (rotation speed) which is the difference between the outputfrequency and the frequency of the frequency signal used for the detection is created, the frequency of the vector of when the output frequency becomes a set value is computed in advance, a voltage signal corresponding to the difference between the vector frequency and the computed frequency is fed back to the voltage-controlled oscillating section when the voltage-controlled oscillating section is driven so as to make the difference zero, thereby forming a PLL. Therefore, when the PLL is locked, the output frequency is adjusted to a set frequency. After the PLL is locked and if the difference between the output frequency and the set frequency becomes large, the set value is integrated by an integrating circuit section and the integral is added to the control voltage.