To assess the seismic hazard with temporal change in Taiwan, we developed a new approach which combines both the Brownian passage time (BPT) model and the coulomb stress change, and implements the seismogenic source parameters by the Taiwan Earthquake Model. The BPT model was adopted to describe the rupture recurrence intervals of specific fault sources together with the time elapsed since the last fault rupture to derive their long-term rupture probability. We also evaluated the short-term seismicity rate change based on the static coulomb stress interaction between seismogenic sources. By considering these time-dependent factors, our new combined model, relative to a time-independent model, suggests an increased long-term seismic hazard in the vicinity of active faults along the western coastal plain and the Longitudinal Valley, where active faults have short recurrence intervals and long elapsed time since their last ruptures and/or short-term elevated hazard levels right after the occurrence of large earthquakes due to the stress triggering effect. The stress enhanced by the 6 February 2016 ML 6.6 Meinong earthquake also significantly increased the rupture probabilities of several neighboring seismogenic sources in southwestern Taiwan and raised the hazard level for the near future. Our approach drew upon the advantage of incorporating both long- and short-term models to provide time-dependent earthquake probability constraints. This new model provides more insight than any other models for Taiwan. Thus, it offers decision makers and public officials an adequate basis for rapid evaluations of consequent hazards and for responses to future emergency scenarios such as victim relocation and sheltering.