Instrumental variables (IVs), sources of treatment randomization that are conditionally independent of the outcome, play an important role in causal inference with unobserved confounders. However, the existing IV-based counterfactual prediction methods need well-predefined IVs, while it is an art rather than science to find valid IVs in many real-world scenes. Moreover, the predefined hand-made IVs could be weak or erroneous by violating the conditions of valid IVs. These thorny facts hinder the application of the IV-based counterfactual prediction methods. In this paper, we propose a novel Automatic Instrumental Variable decomposition (AutoIV) algorithm to automatically generate representations serving the role of IVs from observed variables (IV candidates). Specifically, we let the learned IV representations satisfy the relevance condition with the treatment and exclusion condition with the outcome via mutual information maximization and minimization constraints, respectively. We also learn confounder representations by encouraging them to be relevant to both the treatment and the outcome. The IV and confounder representations compete for the information with their constraints in an adversarial game, which allows us to get valid IV representations for IV-based counterfactual prediction. Extensive experiments demonstrate that our method generates valid IV representations for accurate IV-based counterfactual prediction.