The applications of terahertz (THz) technology can be greatly extended using non-diffractive beams with unique field distributions and non-diffractive transmission characteristics. Here, we design and experimentally demonstrate a set of dual non-diffractive THz beam generators based on an all-dielectric metasurface. Two kinds of non-diffractive beams with dramatically opposite focusing properties, Bessel beam and abruptly autofocusing (AAF) beam, are considered. A Bessel beam with longdistance non-diffractive characteristics and an AAF beam with low energy during transmission and abruptly increased energy near the focus are generated for x- and y-polarized incident waves, respectively. These two kinds of beams are characterized and the results agree well with simulations. In addition, we show numerically that these two kinds of beams can also carry orbital angular momentum by further imposing proper angular phases in the design. We believe that these metasurface-based beam generators have great potential use in THz imaging, communications, non-destructive evaluation, and many other fields. [Figure not available: see fulltext.].