Tsunami-induced disasters present a significant threat to coastal communities. Under the effects of sea-level rise due to climate change, tsunami occurrence frequency and intensities would increase in a nonstationary manner due to the long-term progressive trend in the variability in sea level. Therefore, the reliability of coastal infrastructure systems affected by tsunami hazard will diminish over time. A procedure for hazard assessment that integrates tsunamis occurring at random times with evolving sea-level rise should be established. This paper presents a novel framework for the time-variant assessment of tsunami hazard considering the effects of nonstationary sea-level rise due to climate change based on a non-Poisson stochastic renewal process. A time-variant probabilistic sea-level rise is modeled by utilizing various climate models and existing data reported in several studies. The conditional tsunami hazard curves considering sea-level rise are estimated by performing tsunami propagation analyses under different sea-level rise cases and by Monte Carlo simulation, considering the uncertainties associated with earthquake fault movements. Finally, the new concept of time-variant tsunami hazard assessment considering the nonstationary effects of sea-level rise is developed according to a non-Poisson stochastic renewal process. An illustrative example is provided by applying the proposed framework to several municipalities in the Kochi Prefecture of Japan that are subjected to the anticipated Nankai-Tonankai earthquake. The effects of sea-level rise on time-variant tsunami hazard under Poisson and non-Poisson processes of earthquake occurrence are discussed.