The signal-to-noise ratios (SNR) of various partial response maximum-likelihood (PRML) systems in perpendicular magnetic recording using a multi-layered main-pole head are studied. Among the PRML systems having transfer function (1+D^p)(1−D^q)(1+D^l)^m represented by a delay operator D, several PRML systems which show the large SNR at the discrimination point are found by utilizing the minimum Euclidean distance between all possible pairs of sequences at the input of Viterbi decoder. The required SNRs of the PRML systems to achieve a bit-error rate of 10⁻⁴ are also obtained by computer simulation. It is shown that the PR(1,1,0,0,0,0,−1,−1)ML system with a conventional decoder exhibits the excellent performance and the system with a simplified decoder still shows the good performance at high recording density.