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Stationarity in the relationship between causal variables and target variables is the fundamental assumption of statistical downscaling models. However, we hypothesize that this assumption may not be valid in a changing climate. This study develops a downscaling technique in which the relationship between causal and target variables is considered to be time-varying rather than static. The proposed time-varying downscaling model (TVDM) is utilized to downscale monthly precipitation over India to 0.25 x 0.25 degrees gridded scale using the large-scale outputs from multiple general circulation models (GCMs), namely the Hadley Centre Coupled Model version 3 (HadCM3), coupled Hadley Centre Global Environmental Model version 2-Earth System model (HadGEM2-ES) and Canadian Earth System Model version 2 (CanESM2). Observed precipitation data are obtained from the India Meteorological Department (IMD), Pune. For future projection, the temporal evolution of each of the TVDM parameters is investigated using its deterministic (trend and periodicity) and stochastic components. TVDM is found to outperform the most commonly used statistical downscaling model (SDSM) and regional climate model (RCM) output at all the locations. The Regional Climate Model version 4 (RegCM4) precipitation data (RCM outputs) are obtained from the Coordinated Regional Climate Downscaling Experiment (CORDEX) data portal supplied by Indian Institute of Tropical Meteorology (IITM), Pune. The proposed model (TVDM) differs from the existing stationarity assumption-based approaches in updating the relationship between causal and target variables over time. It is understood that parameter uncertainty is the major issue in consideration of non-stationarity. Still, the TVDM is found to be very useful in the context of climate change due to its time-varying component.