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Let A is a row first-plus-last right circulant matrix and C is a row first-plus-last left circulant matrix which first row is (P 1,P 2,…,P n ), and P n is the Pell number. To investigate the explicit determinants of those matrices, we adopted some special transformation between polynomial and multiplication and explicit representation of Binet formula in this paper. Putting the transformation into use when computing the determinant of matrix, the explicit determinants of matrices A and C are given only by the Pell and Pell-Lucas numbers. The result is very useful in the information theory such as generalized cyclic codes, graph disposing and so on.