This paper studies a high order moments portfolio optimization model with transaction costs. The model takes kurtosis as objective function and takes the skewness, variance, mean and transaction costs as constraints conditions. Since the optimization problem is of high order and non-convex, it brings some difficulties to the solution of the model. Therefore, this paper transforms the optimization problem into a semi-definite matrix optimization problem by using the moment matrix theory, and then solves it. Through the study of four risky assets in China’s securities market, it is found that transaction costs are significant parts in the study of portfolio model. In addition, sensitivity analysis shows that the kurtosis and skewness are positively correlated with the mean and variance invariant. When mean and skewness are constant, kurtosis and variance are positively correlated. When mean and skewness remain unchanged, the fourth order standard central moment and variance are negatively correlated.