In order to meet the testing requirements of task scheduling algorithms, this paper proposes two algorithms for generating random adjacency matrixes. One algorithm is used for generating random adjacency matrixes representing either directed cyclic graphs or directed acyclic graphs. The other algorithm is used for generating directed acyclic graphs only. The paper analyses the characters of elements of an adjacency matrix, and applies a square matrix with elements falling into a Gaussian distribution and the technique of descending order to achieve a random adjacency matrix. We conduct experiments on our algorithms using MATLAB. The experimental results show that the algorithms have high efficiencies, and adjacency matrixes which represent task graphs with dozens of nodes and dozens of edges can be generated in one minute. Those random adjacency matrixes generated by the algorithms are suited for task scheduling algorithms which use random adjacency matrixes to verify validities.