Timely and reliable estimation of electricity power consumption (EPC) is essential to the rational deployment of electricity power resources. Nighttime stable light (NSL) data from the Defense Meteorological Satellite Program Operational Linescan System (DMSP-OLS) have the potential to model global 1-km gridded EPC. A processing chain to estimate EPC includes: (1) NSL data correction; and (2) regression model between EPC statistics and NSL data. For the global gridded EPC estimation, the current approach is to correct the global NSL image in a uniform manner and establish the linear relationships between NSL and EPC. However, the impacts of local socioeconomic inconsistencies on the NSL correction and model establishment are not fully considered. Therefore, in this paper, we propose a novel locally adaptive method for global EPC estimation. Firstly, we set up two options (with or without the correction) for each local area considering the global NSL image is not saturated everywhere. Secondly, three directions (forward, backward, or average) are alternatives for the inter-annual correction to remove the discontinuity effect of NSL data. Thirdly, four optional models (linear, logarithmic, exponential, or second-order polynomial) are adopted for the EPC estimation of each local area with different socioeconomic dynamic. Finally, the options for each step constitute all candidate processing chains, from which the optimal one is adaptively chosen for each local area based on the coefficient of determination. The results demonstrate that our product outperforms the existing one, at global, continental, and national scales. Particularly, the proportion of countries/districts with a high accuracy (MARE (mean of the absolute relative error) <= 10%) increases from 17.8% to 57.8% and the percentage of countries/districts with inaccurate results (MARE > 50%) decreases sharply from 23.0% to 3.7%. This product can enhance the detailed understanding of the spatiotemporal dynamics of global EPC.