There is provided a frequency synthesizer. The frequency synthesizer includes a frequency oscillator adjusting an output frequency according to a control bit; a programmable divider having a preset minimum division ratio, the programming divider dividing the output frequency of the frequency oscillator at a variable division ratio; a counter unit receiving an output signal of the programmable divider and a reference frequency to generate a count value by counting rising edges of the output signal of the programmable divider during one cycle of the reference frequency, and outputting a first hit signal when the count value is 1, and outputting a second hit signal when the count value is 2; and a phase detection unit outputting a control bit obtained by subtracting a fractional error of the output signal of the programmable divider from a fractional error at a locked phase obtained from the count value and the reference frequency.