This paper proposed a test statistic for testing high dimensional mean vector by imposing the linear structure on high dimensional correlation matrices. The proposed test is valid for both the low dimensional setting and high dimensional setting even if the dimension of the data is greater than the sample size. The limiting null distribution of the proposed test statistic is derived. Extensive simulations are conducted for estimating the precision matrix and testing high dimensional mean vector. Simulation results show that the proposed estimation and test perform well compared with the existing methods.