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Let n be a positive integer, and Cn(r) be the set of all n× nr-circulant matrices over the Boolean algebra B ={0, 1}, . For any fixed r-circulant matrix C(C≠0) in Gn. Define an operation "*" in Gn： A * B = ACB for any A, B in Gn, where ACB is the usual product of Boolean matrices. Then （Gn, *）is a semigroup. We denote this semigroup by Gn(C) and call it the sandwich semigroup of generalized circulant Boolean matrices with sandwich matrix C. In this paper, the fully regular elements in Gn(C) are characterized. The algorithm to find all the fully regular elements of A in Gn(C) is given.

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