Conditions for direct amplification of laser light by high energy e-beams are analysed theoretically in depth. The major results are:(1)the movement of high energy electrons in a powerful laser field is a conservative field movement, thus the condition for in-phase coupling is obtained;(2)proper coupling angles is necessary to insure the electro-magnetic wave to obtain energy from e-beams. It is pointed out that this new FEL is feasible.