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We present a silicon dual-coupled-ring resonator modulator with push-pull coupling tunings. The basic idea of this scheme is to construct a dual-coupled-ring resonator structure in which the coupling coefficients of all coupling regions are tunable through Mach-Zehnder interferometers operated in push-pull modes. Two coupling coefficients are tuned jointly for optical bandwidth shaping and tuning while another coupling coefficient is tuned for high speed and chirp-free modulation. The fundamental analytical expressions for the intensity transmittance, the critical and the resonance conditions of the proposed dual-coupled-ring resonator modulator are derived. In addition, the performance simulations and optimization are presented and compared with those of the single-ring resonator modulator. The proposed dual-coupled-ring resonator modulator is more likely to achieve wide optical bandwidth tuning range and narrow channel spacing simultaneously, which are suitable for future optical processing and interconnects.