［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.