Continuous-time Markov chains (CT-MCs) is a basic mathematical model, which plays a central role in stochastic modeling. The reduction problem is one of the important research questions. Bisimulation introduced in concurrency and computer science is a commonly used tool in reduction. Recently, the scale reductions of CT-MCs and continuous-time control Markov chains (CT-CMCs) have been investigated based on bisimulations. However, the data used to construct CT-MCs is often imprecision by reality. To overcome this problem and better reduce CT-MCs, approximate bisimulations are introduced to study the reduction problem of CT-MCs. Firstly, giving the definition of $\epsilon$-bisimulation of CT-MCs, where $\epsilon\in[0,1]$, which considers the two states of which behaviors with the difference not exceeding $\epsilon$ as equivalent rather than being the same. For CT-CMCs, the notion of $\epsilon$-forward-backward bisimulation is introduced to analysis the controllability, which not only considers the successor neighborhoods but also the predecessor neighborhoods. Then, the algorithms for the maximal $\epsilon$-forward-backward bisimulation which is an equivalence relation are provided and the maximum controllable quotient set contained in the equivalence relation is computed. Finally, the quotients of CT-MCs are constructed, which are CT-MCs with fewer states, and the consistency between the asymptotic stabilities of a CT-CMC and its quotient is obtained. The quotients of CT-CMCs are constructed, which are CT-CMCs with fewer states, and the consistencies between a CT-CMC and its quotient in asymptotic stabilities and controllabilities are developed.