We present measurements of the top quark mass using mT2, a variable related to the transverse mass in events with two missing particles. We use the template method applied to tt dilepton events produced in pp collisions at Fermilab's Tevatron Collider and collected by the CDF detector. From a data sample corresponding to an integrated luminosity of 3.4  fb−1, we select 236 tt candidate events. Using the mT2 distribution, we measure the top quark mass to be Mtop=168.0+4.8−4.0(stat)±2.9(syst)  GeV/c2. By combining mT2 with the reconstructed top quark mass distributions based on a neutrino weighting method, we measure Mtop=169.3±2.7(stat)±3.2(syst)  GeV/c2. This is the first application of the mT2 variable in a mass measurement at a hadron collider.