  Combining an optimized expansion scheme in the spirit of the background field
method with the Coleman's normal-ordering renormalization prescription, we
calculate the effective potential of sine-Gordon field theory beyond the
Gaussian approximation. The first-order result is just the sine-Gordon Gaussian
effective potential (GEP). For the range of the coupling beta^2 <= 3.4 pi (an
approximate value), a calculation with Mathematica indicates that the result up
to the second order is finite without any further renormalization procedure and
tends to improve the GEP more substantially while beta^2 increases from zero.
