Causal inference from observational data is highly regarded for revealing the underlying operational mechanisms, where counterfactual inference has emerged as a prominent concern. The principal challenge of counterfactual inference lies in the elimination of confounding bias. While various advanced models for de-confounding of observed confounders are proposed, the significant gaps come from unobserved confounders, which distort the accuracy of inference. In this paper, we propose a novel variational learning model of unobserved confounders for counterfactual inference (VLUCI), which obviates the unverifiable unconfoundedness assumption commonly presupposed by most causal inference methods. Specifically, through the disentanglement of the direct causal effects of observed covariates, an interacting doubly variational learning model based on treatment and outcome variables is constructed to approximate the distribution of unobserved confounders, thereby enabling the precise counterfactual inference. The VLUCI adapts to both discrete and continuous treatment. Extensive experiments on synthetic dataset and real-world trials demonstrate the superior performance of VLUCI in inferring unobserved confounders and enhancing the accuracy of counterfactual inference. Additionally, VLUCI provides confidence intervals for counterfactual outcomes, aiding decision-making in risk-sensitive domains.