Energy poverty has a remarkable impact on socioeconomic development and human health. To identify energy poverty and further explore its influencing factors, this study uses 8239 households from 25 provinces from the China Family Panel Studies (CFPS) as the research object. First, the household energy poverty index (EPI) from 2012 to 2016 is measured. Second, the partially linear functional-coefficient (PLFC) model, which can capture individual heterogeneity, is employed to investigate how renewable energy technology innovation (RETI) alleviates energy poverty, also examining the role of marketization in the alleviation effect. The findings are as follows: (1) RETI significantly alleviates household energy poverty; (2) the alleviation effect of RETI on household EPI is affected by the marketization level (ML). In particular, when the ML is greater than 5.94, the alleviation effect is stronger; (3) under the influence of the ML, the alleviation effect exhibits a significant spatial heterogeneity. The eastern provinces exhibit the most significant alleviation effect. Finally, according to the nonparametric relationship between RETI and the EPI, we propose corresponding policy recommendations to alleviate household energy poverty.