This paper studies the asymptotic property and confidence region of Catoni's Z estimator under the finite variance assumption. First, we investigate the CLT for Catoni's Z estimator with the asymptotically optimal variance, if the tuning parameter has order (Formula presented.). Second, we propose the normal approximated confidence region of Catoni's Z estimator. The simulations show that the proposed 99% CLT-based confidence regions are shorter than the existing non-asymptotic confidence regions; mean squared errors of Catoni's Z estimators are typically smaller than sample means from heavy-tailed data. Furthermore, the simulated coverage probabilities of the CLT-based confidence region are close to the confidence levels when the sample size is moderately large. For 6-year DOCVIS data (the number of doctor visits) in the German health care demand dataset, our CLT-based confidence regions are tighter than non-asymptotic confidence regions.