We study the generalized differential entropy based on the joint distribution of eigenvalues of random density matrices. First, based on the paper by Luo Laizhen et al., we calculate the generalized differential entropy under the joint distribution of eigenvalues of Wishart matrices. Then, we use Laplace transform and Laplace inverse transform to calculate the generalized differential entropy under the joint distribution of eigenvalues of random quantum states and the joint distribution of diagonals of random density matrices. On the other hand, the related random matrix model induced by the random quantum state is studied. This model plays an important role in quantum information theory. Finally, the Renyi entropy and Tsallis entropy are taken as examples to verify the generalized differential entropy in three cases, and we promote the results of Luo Laizhen et al.