The inter-track interference (ITI) is a major impairment for the next-generation magnetic recording systems.The single-track read channel model, combined with anti-ITI signal detection schemes, is a general way to recover single-track data from a readback signal corrupted by the ITI. In contrast to the general way, the multi-track read channel model can be used to simultaneously recover multi-track data from a readback signal and we do need not to mitigate the ITI. However, the performance of the multi-track detection is severely degraded by the weak signals from the sidetracks and the indistinguishable symbols. In this paper, to improve this performance, we propose an asymmetric iterative multi-track detection (A-IMD) scheme, which uses two parallel jointed six-symbol-based detectors concatenated with two parallel non-binary low-density parity-check (NB-LDPC) decoder over GF(4) to iteratively recover four tracks' data from the two channel readback signals. Simulation results demonstrate that the performance of the multi-track detection can be greatly improved by using the proposed A-IMD scheme.