This paper treats a band-broadening design technique of a dual-band branch-line coupler with matching networks composed of an impedance step and a short-circuited stub based on the equivalent admittance approach. By replacing each right-handed transmission line (RH-TL) with a composite right/left-handed transmission line (CRLH-TL), very flat couplings over a relative bandwidth of about 10% can be obtained at two arbitrary operating frequencies in comparison with previous CRLH-TLs branch-line couplers. Furthermore, by adding periodical open-circuited stubs into RH-TLs of the designed CRLH-TLs branch-line coupler with matching networks, the entire size of the coupler can be reduced to about 50%. Verification of these band-broadening and size-reduction design techniques can be also shown by an electromagnetic simulation and experiment.