Estimating effective connectivity from functional magnetic resonance imaging (fMRI) time series data has become a very hot topic in neuroinformatics and brain informatics. However, it is hard for the current methods to accurately estimate the effective connectivity due to the high noise and small sample size of fMRI data. In this paper, we propose a novel framework for estimating effective connectivity based on recurrent generative adversarial networks, called EC-RGAN. The proposed framework employs the generator that consists of a set of effective connectivity generators based on recurrent neural networks to generate the fMRI time series of each brain region, and uses the discriminator to distinguish between the joint distributions of the real and generated fMRI time series. When the model is well-trained and generated fMRI data is similar to real fMRI data, EC-RGAN outputs the effective connectivity by means of the causal parameters of the effective connectivity generators. Experimental results on both simulated and real-world fMRI time series data demonstrate the efficacy of our proposed framework.