Zero-shot learning is a new paradigm to classify objects from classes that are not available at training time. Zero-shot learning (ZSL) methods have attracted considerable attention in recent years because of their ability to classify unseen/novel class examples. Most of the existing approaches on ZSL works when all the samples from seen classes are available to train the model, which does not suit real life. In this paper, we tackle this hindrance by developing a generative replay-based continual ZSL (GRCZSL). The proposed method endows traditional ZSL to learn from streaming data and acquire new knowledge without forgetting the previous tasks' gained experience. We handle catastrophic forgetting in GRCZSL by replaying the synthetic samples of seen classes, which have appeared in the earlier tasks. These synthetic samples are synthesized using the trained conditional variational autoencoder (VAE) over the immediate past task. Moreover, we only require the current and immediate previous VAE at any time for training and testing. The proposed GRZSL method is developed for a single-head setting of continual learning, simulating a real-world problem setting. In this setting, task identity is given during training but unavailable during testing. GRCZSL performance is evaluated on five benchmark datasets for the generalized setup of ZSL with fixed and incremental class settings of continual learning. Experimental results show that the proposed method significantly outperforms the baseline method and makes it more suitable for real-world applications.