A frequency synthesizer includes a control section; a first signal generator responsive to the control section for selectively outputting one of frequency signals whose frequencies are represented by Fp=a.times..vertline.P.vertline..times..DELTA.F (where the coefficient a is a positive odd number and the coefficient p is an integer); and a second signal generator responsive to the control section for selectively outputting one of frequencies whose frequencies are represented by Fq=b.times..vertline.Q.vertline..times..DELTA.F (where the coefficient b is a positive integer exclusive of integral multiples of prime factors into which a is resolved, and the coefficient Q is an integer and satisfying the expression: .vertline.Q.vertline..ltoreq.(a-1)/2. A mixer mixes a frequency signal Fp from the first signal generator and a frequency signal Fq from the second signal generator; and a frequency selecting circuit selects either of frequency signals .vertline.FP-Fq.vertline. or Fp+Fq output from the mixer. The control section determines the values of P and Q satisfying the following expresion P=T+(S-b.times.Q)/a on the basis of a desired frequency signal Fi=m.times..DELTA.F, a coefficient m=0, 1, 2, ..n set in predetermined frequency .DELTA.F; and quotient T and remainder s of m/a to cause each of the first and second signal generators to output a predetermined frequency and the frequency selecting circuit to select one of the frequency signals .vertline.Fp-Fq.vertline. and Fp+Fq that corresponds to the frequency signal Fi.