Higgs is the only scalar field in the standard model of particle physics (SM), which makes it possible for the Higgs to play another important role in the early universe to drive inflation. The most successful model of Higgs inflation introduces a large non-minimal coupling between the Higgs and the Ricci scalar that, however, largely lowers the cutoff scale of the theory. The low cutoff causes the unitarity problem in the model, especially during the violent preheating stage. This fact calls for a UV-extension of the model. One of the possibilities is to introduce an R^2 term, so called the mixed Higgs-R^2 model. In this talk, I will briefly review the inflation dynamics in the mixed Higgs-R^2 model, and then introduce the preheating stage after inflation. Specifically, I will explain the reduction of the violent spike preheating in the Higgs inflation due to the presence of R^2 as well as the possibility to realize tachyonic preheating in the mixed Higgs-R^2 model.