Abstract: This paper studies the generalized inverse spectrum problem of a kind of symmetric pentadiagonalmatrix plus arrow matrix.First，the extreme eigenvalues of all principal submatrixes of thematrix are taken as their characteristic data.Second，the geometric properties of conic curve，pentadiagonalmatrix and arrow matrix are employed to reconstruct this kind of special arrow banded matrix.Finally，the sufficient conditions for the solution of the problem and the algorithm and examples of the problem construction are given，and the accuracy of the results is verified.