In this study, in order to monitor meteorological droughts of the Qazvin station in Iran, drought duration and severity using historical monthly precipitation during 1964–2015 and copula functions is investigated. The characteristics of drought are computed from monthly standardized precipitation index (SPI). Different univariate distributions were fitted to characteristics of drought. According to the Kolmogorov-Smirnov goodness-of-fit test, exponential and gamma distributions were selected as appropriate for drought duration and severity, respectively. For bivariate drought analysis, five copula functions (i.e., Gumbel Hougaard, Galambos, Frank, Plackett, and Clayton) were utilized and statistical measures including root mean squared error (RMSE), maximum log-likelihood (MLL), Akaike information criterion (AIC), and Nash-Sutcliffe coefficient (NSC) were computed. Among different functions, the Galambos copula with a maximum value of NSC (0.939) and minimum values of RMSE (0.0649) and AIC (720.781) were selected as the best one for bivariate drought analysis. Genetic algorithm (GA) was used for estimation of the Galambos copula parameter and the results compared with the inference function marginals (IFM) method. The RMSE value for the copula-based GA method obtained as 0.0567 shows the superiority of GA compared with the IFM (RMSE = 0.0649). Using the Galambos copula function, the return periods and conditional probability of drought events over the study region were determined. Such probabilistic characteristics of drought can be used for water resources management and planning.