Methods proposed in the literature for zero-shot learning (ZSL) are typically suitable for offline learning and cannot continually learn from sequential streaming data. The sequential data comes in the form of tasks during training. Recently, a few attempts have been made to handle this issue and develop continual ZSL (CZSL) methods. However, these CZSL methods require clear task-boundary information between the tasks during training, which is not practically possible. This paper proposes a task-free (i.e., task-agnostic) CZSL method, which does not require any task information during continual learning. The proposed task-free CZSL method employs a variational autoencoder (VAE) for performing ZSL. To develop the CZSL method, we combine the concept of experience replay with knowledge distillation and regularization. Here, knowledge distillation is performed using the training sample's dark knowledge, which essentially helps overcome the catastrophic forgetting issue. Further, it is enabled for task-free learning using short-term memory. Finally, a classifier is trained on the synthetic features generated at the latent space of the VAE. Moreover, the experiments are conducted in a challenging and practical ZSL setup, i.e., generalized ZSL (GZSL). These experiments are conducted for two kinds of single-head continual learning settings: (i) mild setting-: task-boundary is known only during training but not during testing; (ii) strict setting-: task-boundary is not known at training, as well as testing. Experimental results on five benchmark datasets exhibit the validity of the approach for CZSL.