  Determinantal point processes (DPP) serve as a practicable modeling for many
applications of repulsive point processes. A known approach for simulation was
proposed in \cite{Hough(2006)}, which generate the desired distribution point
wise through rejection sampling. Unfortunately, the size of rejection could be
very large. In this paper, we investigate the application of perfect simulation
via coupling from the past (CFTP) on DPP. We give a general framework for
perfect simulation on DPP model. It is shown that the limiting sequence of the
time-to-coalescence of the coupling is bounded by $K|\Lambda|\log K|\Lambda|$.
An application is given to the stationary models in DPP.
