This paper analyzes the sampled-data model of n-th order integrator in the case of a first-order hold (FOH). Also, the corresponding FOH discretization pulse transfer function and sampling model in normal form are derived. On the basis of these results, we present discrete system zeros and sampling zeros which their asymptotic properties are obtained. In additional, stability of discrete-time zeros for n-th order integrator model is represented as the sampling period T tends to zero. It is a further extension of corresponding results.