Poisson process is one of stochastic process that is useful in modeling real phenomena. The cyclic Poisson process is a process where the Poisson component having periodic intensity function. This process is very appropriate in describing phenomena that occur periodically. This research consider the waiting time of cyclic Poisson process. The waiting time for the m^th event of a Poisson process is the length of time since the process is observed until the m^th event occurs. There is no assumption about any particular parametric form of the intensity function of the cyclic Poisson process. This research consider the situation when there is only a single realization of the cyclic Poisson process is observed in a bounded interval. The objectives of this research are to construct estimators of the distribution and density functions of waiting time of cyclic Poisson process, and to prove the consistency of the propose estimators. The results of this research show that the propose estimators are consistent.