The existence of nontrivial solutions and positive solutions for fractional Laplace systems with Dirichlet boundary conditions was investigated.According to the features when the Dirichlet boundary conditions of fractional Laplace systems are satisfied and based on the mountain pass theorem, embedding theorem, dominated convergence theorem and Brezis-Leb lemma in Sobolev space, the Palais-Smale compactness conditions of the energy functional were proved.Then the existence of nontrivial solutions for fractional Laplace systems with Dirichlet boundary conditions was concluded.Moreover, The Nehari manifold and minimal energy method were used to prove the existence of positive solutions for fractional Laplace systems with Dirichlet boundary conditions.