We consider the problem of estimating the mean function of a compound cyclic Poisson process in the presence of power function trend. The objectives of this paper are: (i) to construct confidence interval for the mean function of a compound cyclic Poisson process with significance level , (ii) to prove that the probability that the mean function contained in the confidence interval converges to , and (iii) to observe, using simulation study, that the probabilities of the mean function contained in the confidence intervals for bounded length of observation interval. The main results are a confidence interval for the mean function and a theorem about convergence of the probability that the mean function contained in confidence interval. The simulation study shows that the probability that the mean function contained in the confidence interval is in accordance with the theorem. The contribution of this study is to provide information for users regarding confidence interval for the mean function of a compound cyclic Poisson process in the presence of power function trend.