A novel dualband impedance transformer based on fractional-order inductor and capacitor is proposed in this paper. This transformer is designed to transfer the arbitrary frequency-dependent complex impedances sources to loads at two irrelevant frequencies with one fractional-order inductor and two fractional-order capacitors. Each fractional-order element has two parameters to be determined: the order of the element, which is a discrete number, and its coefficient, which is a continuous numbers. The standard particle swarm optimization algorithm is improved to adapt the simultaneous mixed continuous and discrete variables optimization. The continued fraction expansion method is employed to approximate the fractional-order element characteristics which response is proportional to an arbitrary order of the frequency. An RC network is built to verify the proposed method's effects after each fractional-order element synthesized by the Cauer network synthesis method. The agreement of the calculation and simulation results shows that the proposed transformer has successfully transferred the frequency-dependent complex impedances from sources to loads at two frequencies.