In this paper, we consider the problem of responding to a count query (or any other integer-valued queries) evaluated on a dataset containing sensitive attributes. To protect the privacy of individuals in the dataset, a standard practice is to add continuous noise to the true count. We design a differentially-private mechanism which adds integer-valued noise allowing the released output to remain integer. As a trade-off between utility and privacy, we derive privacy parameters $\eps$ and $δ$ in terms of the the probability of releasing an erroneous count under the assumption that the true count is no smaller than half the support size of the noise. We then numerically demonstrate that our mechanism provides higher privacy guarantee compared to the discrete Gaussian mechanism that is recently proposed in the literature.