The compound Poisson process S-N(t) = Sigma(N(t))(j=1) X (j) has been widely used in many fields, for example, physics, engineering, finance, and so on. Regarding the process, the average number, namely t(-1)E[S-N(t)] = lambda mu, attracts lots of interests. In this article, we derive the limiting behavior of the log empirical likelihood ratio statistic for lambda mu when the population is in the domain of attraction of normal law. The simulation studies confirm the theoretical result.