In this paper, we extend two efficient computational algorithms for the determinant evaluation of general cyclic heptadiagonal matrices with Toeplitz structure. We try to design two numerical algorithms by a certain type of matrix reordering in matrix partition and another algorithm by using the transformation of a block upper triangular transformation for the cyclic heptadiagonal Toeplitz matrices. The cost of these algorithms is about \(11n+O(\hbox {log}\,n)\) for computing \(n\hbox {th}\) order cyclic heptadiagonal Toeplitz determinants. Some numerical experiments are presented to demonstrate the performance and effectiveness of the proposed algorithms with other published algorithms.