Abstract:[Purposes]The transmission eigenvalue problem is very important for inverse problems. [Methods]The transmission eigenvalue problem of Maxwel’s equations with impedance boundary condition in penetrable, nonmagnetic and nonuniform media was studied by using the boundary integral equation method. [Results]The impedance-magnetic boundary trace operator was constructed, and the impedance magnetic boundary trace operator was expressed by the boundary integral operator. [Conclusions]It is proved that one kind of boundary integral operator is coercive, another kind of boundary integral operator is compact, and the difference operator of impedance magnetic boundary trace operator is a Fredholm operator with index zero and analytic.