Predicting time-varying counterfactual outcomes based on observational data is significant in various fields. However, current state-of-the-art methods face dual challenges of low prediction accuracy and low computational efficiency in long sequence scenarios, and existing balancing strategies have obvious limitations in balancing bias and error. To this end, this study proposes Causal Mamba, a novel end-to-end deep learning framework based on Mamba for predicting time-varying counterfactual outcomes. The framework integrates a Treatment-Covariate-Outcome parallel Mamba module (TCO-TriMamba block) and an adversarial-reconstruction multi-task balancing strategy. The TCO-TriMamba block can efficiently identify and focus on key components from historical information. By optimizing multiple tasks in coordination with this module, the adversarial-reconstruction multi-task balancing strategy effectively adjusts to time-varying confounders while ensuring the accuracy of counterfactual prediction tasks. Experimental results demonstrate that Causal Mamba outperforms existing benchmark models in multi-step counterfactual prediction tasks, yielding significantly higher prediction accuracy and shorter running time especially in long sequence scenarios.