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This paper presents a feedback canceller (FC) for T-DMB repeaters. Though the conventional FC of T-DMB repeaters has a good feedback cancellation performance, it distorts the recovered signal's out-band spectrum. This spectrum distortion problem is very crucial for commercializing T-DMB repeaters. The feedback canceller with pre-whitening filters (PWFs), which estimates the feedback channel using whitened input signals, can compensate this spectrum problem. However the feedback canceling performance degradation occurs when the feedback channel varies with Doppler effects. To compensate the out-band spectrum distortion and cope with the variation of feedback channel, we propose a novel FC based on the convex combination algorithm. Simulation results show that the proposed FC can remove clearly the out-band spectrum distortion of the recovered signal with improved the feedback canceling performance in both time-invariant and time-varying feedback channels.