This paper explains the characteristic polynomial and eigenvalues of the antiadjacency matrix of a directed cyclic dumbbell graph. Antiadjacency matrix of a directed graph is a matrix whose entries represent whether there exist a directed edge connecting two vertices in the directed graph or not. The coefficients of the characteristic polynomial of the antiadjacency matrix of directed cyclic dumbbell graph is obtained by evaluating the determinant of each induced subgraph of the directed cyclic dumbbell graph and by counting the number of certain forms of induced subgraph of the directed cyclic dumbbell graph. The eigenvalues of the antiadjacency matrix of directed cyclic dumbbell graph is obtained by polynomial factorization. The result obtained show that the coefficients of the characteristic polynomial and the eigenvalues of antiadjacency matrix of directed cyclic dumbbell graph can be expressed as a function that is dependent to the number of vertices of the cycle subgraphs of directed cyclic dumbbell graph. © 2020 American Institute of Physics Inc.. All rights reserved.