  This paper develops an efficient numerical method for the inverse scattering
problem of a time-harmonic plane wave incident on a perfectly reflecting random
periodic structure. The method is based on a novel combination of the Monte
Carlo technique for sampling the probability space, a continuation method with
respect to the wavenumber, and the Karhunen-Lo$\grave{e}$ve expansion of the
random structure, which reconstructs key statistical properties of the profile
for the unknown random periodic structure from boundary measurements of the
scattered fields away from the structure. Numerical results are presented to
demonstrate the reliability and efficiency of the proposed method.
