Abstarct: In multivariate analysis, one of the most challenging cases of estimating a covariance matrix of a random variable is when the number of variables (‎dimension‎) is large. Also, in some multivariate discussions, it is necessary to estimate the function of a covariance matrix. Suppose p represents the ‎dimension. In this thesis, we examine the covariance matrix estimator and some functions of it for the high ‎dimension (p→∞). In this regard, we assume that the population of sampling has normal and non-normal distribution and introduce non-parametric shrinkage estimators of the covariance matrix in the high dimension and examine some of their properties. Also, using simulation examples, we evaluate the efficiency of the proposed shrinkage estimators for the covariance matrix in the high dimension.