The problem of reflection and transmission of an electromagnetic plane wave incident from a dielectric medium, reflected and transmitted by another dielectric medium which moving in an arbitrary direction is analyzed in detail. The field vectors of the reflected and transmitted waves, and the reflection and transmission coefficients as well as the energy relations are deduced for the reflected, transmitted and incident waves. In particular, the properties of the force exerted on the moving medium by a plane wave are discussed in comparison with the case in which the incident space is free space and some new phenomenon are suggested for notice.