  Effective mass Klein-Gordon equation for the asymmetric Hulth{\'e}n potential
is solved in terms of hypergeometric functions. Results are obtained for the
scattering and bound states with the position dependent mass and constant mass,
as a special case. In both cases, we derive a condition for the existence of
transmission resonance (T=1). We also study how the transmission resonance
depends on the particle energy and the shape of the external potential.
