Abstract: In this paper, we discuss some important properties of T-IPH distribution, where T-IPH denotes the infinite phase type distribution defined on a discrete-time birth and death process with countably many states. For the distribution, we firstly give the probability generating function (PGF), then the obtained results enable us to further give the recursive formula to calculating numerical results of distributional law and factorial moment for the distribution. Finally, we also give an application of T-IPH distribution in queueing systems.