Let k be a nonzero complex number. We consider a k-circulant matrix whose first row is (J1, J2, . . . , Jn), where Jn is the n th Jacobsthal number, and obtain the formulae for the eigenvalues of such matrix improving the formula which can be obtained from the result of Y. Yazlik and N. Taskara [J. Inequal. Appl. 2013, 2013:394, Theorem 7]. The obtained formulae for the eigenvalues of a k-circulant matrix involving the Jacobsthal numbers show that the result of Z. Jiang, J. Li, and N. Shen [WSEAS Trans. Math. 12 (2013), no. 3, 341–351, Theorem 10] is not always applicable. The Euclidean norm of such matrix is determined. We also consider a k-circulant matrix whose first row is (J −1 1 , J−1 2 , . . . , J−1 n ) and obtain the upper and lower bounds for its spectral norm