We introduce a new type of optical beam that can autofocus multiple times in free space, namely, a multi-focus autofocusing optical beam. Based on the superposed caustic method, we design and construct one-dimensional autofocusing optical beams by tailoring and overlapping two paraxial accelerating optical beams. The two accelerating optical beams are shaped in cosine trajectories symmetrically, thus enabling an on-axis multi-focus property. Furthermore, we fabricate compact devices utilizing diffractive optical elements on a quartz plate patterning the required phase for generations of three-focus and four-focus autofocusing optical beams in free space. We expect that this work may bring autofocusing optical beams further potential applications in particle transporting, material processing, and lithography technology.