Duration calculus is a kind of interval temporal logic, which is designed for specifying and reasoning the properties about the embedded real-time systems and hybrid systems. Extend linear duration invariants (ELDI) is an important subset of duration calculus. In this study, a bounded model checking algorithm of ELDI formulas against real-time automaton is proposed. The bounded model checking problem of ELDI is reduced into the validity problem of Quantified linear real arithmetic (QLRA) formulas, which can be solved by Quantifier elimination (QE) technique. Firstly, by using deep first search algorithm, the real-time automaton is searched to find all the symbolic paths segments which satisfy the constraints of observation time length. Secondly, the paths segments are transformed into QLRA formulas. Finally, the QLRA formulas are solved by QE tools. Thus, compared with the related works, a verification algorithm of ELDIs is proposed against real-time automaton with lower complexity. In addition, the practical speed of verifying process is accelerated.