An iterative inter-track interference (ITI) cancelling scheme is described for multi-track signal detection in nonbinary (NB)-LDPC-coded two-dimensional magnetic recording. The multi-track iterative ITI canceller that we propose consists of multi-track soft interference cancellers (SICs), two-dimensional partial response (TDPR) filters, noise-predictive max-log-MAP detectors, and an NB-LDPC decoder. TDPR filters using an ITI-suppressing tap-weight vector mitigate ITI in the first iteration. Multi-track SICs and TDPR filters adjusted to the residual two-dimensional ISI signals efficiently detect multi-track signals in the latter iterations. The simulation results demonstrated that our proposed iterative multi-track ITI canceller achieves frame error rates close to those obtained in a non-ITI case in media-noise-dominant environments when the both-side off-track ratio is up to 50%.