Time-varying counterfactual prediction (TCP) from observational data supports the answer of when and how to assign multiple sequential treatments, yielding importance in various applications. Despite the progress achieved by recent advances, e.g., LSTM or Transformer based causal approaches, their capability of capturing interactions in long sequences remains to be improved in both prediction performance and running efficiency. In parallel with the development of TCP, the success of the state-space models (SSMs) has achieved remarkable progress toward long-sequence modeling with saved running time. Consequently, studying how Mamba simultaneously benefits the effectiveness and efficiency of TCP becomes a compelling research direction. In this paper, we propose to exploit advantages of the SSMs to tackle the TCP task, by introducing a counterfactual Mamba model with Covariate-based Decorrelation towards Selective Parameters (Mamba-CDSP). Motivated by the over-balancing problem in TCP of the direct covariate balancing methods, we propose to de-correlate between the current treatment and the representation of historical covariates, treatments, and outcomes, which can mitigate the confounding bias while preserve more covariate information. In addition, we show that the overall de-correlation in TCP is equivalent to regularizing the selective parameters of Mamba over each time step, which leads our approach to be effective and lightweight. We conducted extensive experiments on both synthetic and real-world datasets, demonstrating that Mamba-CDSP not only outperforms baselines by a large margin, but also exhibits prominent running efficiency.