We propose a general strategy for synthesizing controllable three-dimensional structured array beams. With it, we create a class of beams termed three-dimensional Gaussian array beams and analyze their propagation characteristics. Experimental results are in good agreement with theoretical predictions, demonstrating periodic intensity distributions of the three-dimensional Gaussian array beams in both the transverse plane and propagation direction. Furthermore, by adjusting the initial beam parameters, it is possible to flexibly control both the number and axial position of the array layers along the transmission direction, as well as the transverse spectral density distribution. This strategy holds promise for applications in multi-target optical trapping, attacking, and related optical manipulation scenarios.