Estimating and assessing the variance-covariance matrix (risk) of a large portfolio is an important topic both in financial econometrics and risk management. Ing and Lai (2011) proposed the novel technique, Orthogonal Greedy Algorithm (OGA), with higher accuracy and less computational cost to deal with the estimation error in high dimensional (large) matrix. In this paper, we adopt OGA on Markowitz minimum variance optimization by increasing the accuracy of the high dimensional matrix estimation to obtain the pure theoretical optimal and corresponding expected return. Here, p and n denote the number of stocks and that of historical data, respectively. First, we generate the simulated data which mimic the theory distribution of financial return data to compare the accuracy of the OGA and the thresholding method in Chen, Huang, and Pan (2015). The simulation result shows that the OGA with lower estimation error and higher stability than the thresholding method, especially in great distance between p and n. Second, we randomly select 100 (200, 300) stocks to form the portfolio as the investment target during 1980 to 2016. After assessing the performance of portfolio, the OGA method has higher portfolio expected return, higher Sharpe ratio on average, and higher cumulated investment return than naïve 1/N strategy.