A low frequency solution to the diffraction problem of an E-polarized plane wave incident on a dielectric-loaded slit in a perfectly conducting plane is obtained. The dielectric loading consists of a circular cylinder just filling the slit and concentric with the slit center. The method used is a significant improvement over the traditional pseudo-power-series method of solution. Thus, when the dielectric is absent, our values differ by less than 2.1% from the exact Mathieu function solution at ka = 2.4, a being the half width of the slit. The gap between the high and low frequency solutions has therefore been bridged. When a dielectric is present, the limit ka = 2.4 will be multiplied by 1/∈1/21. It is found that the transmission usually increases with the dielectric constant. Some curves are given to illustrate the effects.