The block experiments have been widely used in sciences, medical and engineering. Universal optimal block designs under general correlation structures are usually difficult to specify theoretically or algorithmically. However, they can sometimes be found for a specific correlation with particular parameter values. There are different correlation structures for the observations which are considered by many researchers. Hub correlation structure has widely application in some network and other similar experiments (see Zhu and Coster [43]). According to the correlation values, there are some different cases for this correlation structure. In this Thesis, we consider two different cases of hub correlation structure and we present a method to construct the universally optimal block designs without using the semibalanced array (SBA) method.