In a changing climate, drought indices as well as drought definitions need to be revisited, because some statistical properties, such as long-term mean, of climate series may change over time. The study aims to develop a Non-stationary Standardized Precipitation Evapotranspiration Index (NSPEI) for reliable and robust quantification of drought characteristics in a changing environment. The proposed indicator is based on a non-stationary log-logistic probability distribution, assuming the location parameter of the distribution is a multivariable function of time and climate indices, as covariates. The optimal non-stationary model was obtained using a forward selection method in the framework of Generalized Additive Models in Location, Scale and Shape (GAMLSS) algorithm. The Non-stationary and Stationary forms of SPEI (i.e. NSPEI and SSPEI) were calculated using the monthly precipitation and temperature data of 32 weather stations in Iran for the common period of 1964–2014. The results showed that almost at all the stations studied, the non-stationary log-logistic distributions outperformed the stationary one. Both drought indicators SSPEI and NSPEI significantly differed in terms of spatial and temporal variations of drought characteristics. While SSPEI identified the long-term and continuous drought/wet events, NSPEI revealed the short-term and frequent drought/wet periods at almost all the stations of interest. Finally, it was revealed that NSPEI, compared to SSPEI, was a more reliable and robust indicator of drought duration and drought termination in vegetation cover during the severest drought period (the 2008 drought), and therefore, was suggested as a suitable drought index to quantify drought impact on vegetation cover in Iran.