Abstract: The variational problems of the complete functional in calculus of variations are studied deperding on the arbitrary arguments,arbitrary multivariable functions and arbitrary-order partial derivatives of multivariable functions.The theorem of the variational problems of the complete functional is proposed and proved.The complete Euler equation set is obtained through the introduction of the partial differential operator.The complete Euler equation set contains all kinds of Euler equations of the variational problems.The correctness of the complete Euler equation set is verified with two functional examples.