We define a new temporal logic called CTL[k-QDDC]. It extends CTL with the ability to specify branching pasts and quantitative temporal properties by combining CTL with the logic Quantified Discrete-time Duration Calculus (QDDC). The idea of bounded model checking is also used in this logic. Compared to CTL, the added expressive power is necessary for specification and verification of real-time distributed software and hardware systems. We give the syntax and semantics of CTL[k-QDDC], discuss its expressive power,and propose an explicit model checking algorithm for Kripke structure. CTL[k-QDDC] is considered as a foundation of some more complex logics for specifying and verifying continuous-time properties in some appropriate structures.