This work proposes a dithered-digital-mixing background timing-skew calibration method for time-interleaved (TI) analog-to-digital converters (ADCs). Unlike prior digital-mixing methods that limit the input bandwidth or lead the calibration process to a limit cycle, the proposed method enhances the input bandwidth to the Nyquist frequency and guarantees the convergence. This is achieved by a pseudo-random binary sequence generator that produces a dither signal. Practical considerations including thermal noise and the step size of variable delay lines are discussed. Behavioral simulation results demonstrate the effectiveness of the proposed method with an improvement of signal-to-noise-and-distortion ratio from 26.3dB to 52.6dB for a 5GS/s 9b 16-channel TI ADC.