Active learning has been increasingly applied to screening functional materials from existing materials databases with desired properties. However, the number of known materials deposited in the popular materials databases such as ICSD and Materials Project is extremely limited and consists of just a tiny portion of the vast chemical design space. Herein we present an active generative inverse design method that combines active learning with a deep variational autoencoder neural network and a generative adversarial deep neural network model to discover new materials with a target property in the whole chemical design space. The application of this method has allowed us to discover new thermodynamically stable materials with high band gap (SrYF$_5$) and semiconductors with specified band gap ranges (SrClF$_3$, CaClF$_5$, YCl$_3$, SrC$_2$F$_3$, AlSCl, As$_2$O$_3$), all of which are verified by the first principle DFT calculations. Our experiments show that while active learning itself may sample chemically infeasible candidates, these samples help to train effective screening models for filtering out materials with desired properties from the hypothetical materials created by the generative model. The experiments show the effectiveness of our active generative inverse design approach.