A sparse representation-based bistatic inverse synthetic aperture radar (ISAR) imaging method can achieve a high-resolution image of a target with sparse aperture data. However, the bistatic ISAR system is more sensitive to noise than the monostatic one because of its nonmirror reflection geometry. To overcome this drawback, we propose the sparse aperture bistatic ISAR imaging method based on joint sparse model. Considering the joint sparse information of bistatic ISAR echo, a joint sparse imaging model is constructed. Then, the dechirped sparse aperture bistatic ISAR echo after translational compensation is transformed into range fast time and azimuth slow time domains by the joint sparse imaging model, and a corresponding azimuth sparse basis is constructed. Then a joint sparse complex approximate message passing algorithm is proposed to joint sparse imaging model. The joint sparse imaging problem is converted to a block sparse imaging problem by vectorization. Using the relationship between the vectorization of the matrix and the Kronecker product, a matrix iteration structure is proposed to solve the joint sparse model efficiently and accurately. The experimental results based on both scattering point model and electromagnetic calculation model data verify the effectiveness of the proposed imaging method.