We describe a kind of true 3D array of focused vortices with tunable topological charge, called the 3D Dammann vortex array. This 3D Dammann vortex array is arranged into the structure of a true 3D lattice in the focal region of a focusing objective, and these focused vortices are located at each node of the 3D lattice. A scheme based on a Dammann vortex grating (DVG) and a mirror is proposed to provide a choice for changing the topological charge of the 3D Dammann vortex array. For experimental demonstration, a 5×5×5 Dammann vortex array is implemented by combining a 1×7 DVG, a 1×5 Dammann zone plate, and another 5×5 Dammann grating. The topological charge of this Dammann vortex array can be tuned (from -2 to +2 with an interval of +1) by moving and rotating the mirror to select different diffraction orders of the 1×7 DVG as the incident beam. Because of these attractive properties, this 3D Dammann vortex array should be of high interest for its potential applications in various areas, such as 3D simultaneous optical manipulation, 3D parallel vortex scanning microscope, and also parallel vortex information transmission.