The preliminary test (pretest) estimator is an estimator that incorporates a preliminary hypothesis test. Among various types of pretest estimators, the pretest estimator for a univariate normal mean is the simplest and the most fundamental one. However, the construction of confidence interval (CI) has not been studied. Recently, a valid CI for a normal mean was established in the setting of meta-analyses, where the sample size is limited to one ( \(n=1\) ). In this paper, we extend this approach to the setting of sample size \(n \ge 1\) . With this approach, we define an explicit formula of the CI for the univariate normal mean, and derive its finite sample and asymptotic properties. We show that the coverage probability of the CI controls the nominal confidence level. Finally, we analyze a real dataset to illustrate the proposed CI.