In this paper, a three-dimensional (3D) reconstruction algorithm is proposed for space targets with multistatic inverse synthetic aperture radar (ISAR) systems. In the proposed algorithm, target 3D geometry can be obtained by solving the projection equations between the target 3D geometry and ISAR images. Specially, it is no need to perform cross-range scaling. To obtain the projection equations, the algorithm consists of two steps: establishing projection matrix and associating scattering centers. Firstly, observation angles of sensor can be estimated by kinematic formulas and coordinate systems transformation. Using azimuth and elevation angles of sensor relative to target, the projection matrix from target 3D geometry to ISAR images is established. Secondly, an association cost function based on projective transform and epipolar geometry is developed. As the cost function is an assignment with 0-1 linear programming, the Jonker-Volgenant algorithm is used to build a one-to-one correspondence between two scattering centers. Numerical results show the efficiency of the proposed algorithm.