According to the theory of circuit，the admittance of the fractional order RL_α-C_βparallel circuit is obtained.Under the condition of α=β and CR² /L<<1，a simple expression for the resonant frequency of the circuit is obtained.On this basis，a simple expression of the quality factor of the parallel resonant circuit is deduced and discussed.It is shown that the theoretical result is in well agreement with numerical simulation of MATLAB software. Then the law of quality factor with the change of element parameters and fractional order is found.