In this paper,a novel maximum corren-tropy high-order extended Kalman filter(H-MCEKF)is proposed for a class of nonlinear non-Gaussian systems presented by polynomial form.All high-order polynomial terms in the state model are defined as implicit variables and regarded as parameter variables;the original state model is equivalently formulated into a pseudo-linear form with original variables and parameter variables;the dynamic relationship between each implicit variable and all variables is modeled,then an augmented linear state model appears by combing with pseudo-linear state mod-el;similarly,the nonlinear measurement model can be equivalently rewritten into linear form;once again,the statistical characteristics of non-Gaussian modeling error are described by mean value and variance based on their finite samples;combing original measurement model with predicted value regarded as added state measurement,a cost function to solve the state estimation based on max-imum correntropy criterion(MCC)is constructed;on the basis of this cost function,the state estimation problem can be equivalently converted into a recursive solution problem in the form of Kalman filter,in which the filter gain matrix is solved by numerical iteration though its fixed-point equation;illustration examples are presented to demonstrate the effectiveness of the new algorithm.