In this study, a three-dimensional dynamic multi-phase model is developed for the high temperature proton exchange membrane fuel cell (HT-PEMFC) to study its start-up processes. Two different kinds of start-up methods which are constant voltage and constant current density are investigated and compared with each other under the same conditions. It is found that the constant voltage mode can make HT-PEMFC reach its normal operating temperature faster than the constant current density. During both the constant voltage and constant current density conditions, there is liquid water produced in the catalyst layer of the cathode zone because the cell temperature is under 100 degrees C. The effects of surrounding environment are also analyzed and investigated. It is found that the heat convection coefficient has an important influence on the HT-PEMFC start-up process. The final cell temperatures under different conditions are obtained and the start-up durations are compared. To shorten the start-up time, a new non-heating method, variable voltage start-up strategy, is proposed and compared with the traditional assisting heating method. It is shown that the HT-PEMFC start-up performance is improved significantly by using this new variable voltage start-up strategy. Copyright (C) 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.