When censored time-to-event data are used to map quantitative trait loci (QTL), the existence of nonsusceptible subjects entails extra challenges. If the heterogeneous susceptibility is ignored or inappropriately handled, we may either fail to detect the responsible genetic factors or find spuriously significant locations. In this article, an interval mapping method based on parametric mixture cure models is proposed, which takes into consideration of nonsusceptible subjects. The proposed model can be used to detect the QTL that are responsible for differential susceptibility and/or time-to-event trait distribution. In particular, we propose a likelihood-based testing procedure with genome-wide significance levels calculated using a resampling method. The performance of the proposed method and the importance of considering the heterogeneous susceptibility are demonstrated by simulation studies and an application to survival data from an experiment on mice infected with Listeria monocytogenes.