Despite recent developments that allowed neural networks to achieve impressive performance in a wide range of recognition, these models are intrinsically challenged by real-world applications. Open-set recognition is introduced to facilitate the development of recognition systems towards real-world applications, for this it has to deal with the issue caused by discriminative features. Such features arise from closed-set training and tend to partition the full input space into the closed set of target classes. To reduce the issue, we present an invertible model, iCausalOSR, to learn invertible causal disentanglement to reveal the essence of classes for open-set recognition. The invertible model consists of an encoder and class functions, wherein the class functions are responsible to model the known classes, and the encoder is responsible for progressive signal separation and contraction. A contrast strategy is designed to couple the encoder and class functions to learn invertible causal disentanglement. The dual properties of the model, causal disentanglement and invertibility, constitute the key elements in revealing the class essence. Experiments on widely-used standard datasets in open-set recognition demonstrate the superior performance of our model.