In this paper, we propose a new method to estimate and effectively reduce the effect of thermal asperity (TA) in the perpendicular magnetic recording (PMR) channels with the state trellis. The TA is estimated from the state trellis, then its average is used to modify the equalized signal entering the Viterbi detector. For the partial response (PR) targets with DC component, the proposed method with a maximum-likelihood detector can improve the bit error rate performance by more than an order of magnitude when TA occurs and degrades when the giant magneto-resistive (GMR) nonlinearity and base line wander (BLW) effects are present. Unlike the previous studies, this method allows the use of PR targets with DC component under the presence of TA.