We theoretically and numerically investigate the generation and evolution of different pulsed terahertz (THz) singular beams with an ultrabroad bandwidth (0.1–40 THz) in long gas-plasma filaments induced by a shaped two-color laser field, i.e., a vortex fundamental pulse (ω0) and a Gaussian second harmonic pulse (2ω0). Based on the unidirectional propagation model under group-velocity moving reference frame, the simulating results demonstrate that three different THz singular beams, including the THz necklace beams with a π-stepwise phase profile, the THz angular accelerating vortex beams (AAVBs) with nonlinear phase profile, and the THz vortex beams with linear phase profile, are generated. The THz necklace beams are generated first at millimeter-scale length. Then, with the increase of the filament length, THz AAVBs and THz vortex beams appear in turn almost periodically. Our calculations confirm that all these different THz singular beams result from the coherent superposition of the two collinear THz vortex beams with variable relative amplitudes and conjugated topological charges (TCs), i.e., +2 and −2. These two THz vortex beams could come from the two four-wave mixing (FWM) processes, respectively, i.e., ω0+ω0−2ω0→ωTHz and –(ω0+ω0) + 2ω0→ωTHz. The evolution of the different THz singular beams depends on the combined effect of the pump ω0−2ω0 time delay and the separate, periodical, and helical plasma channels. And the TC sign of the generated THz singular beams can be easily controlled by changing the sign of the ω0−2ω0 time delay. We believe that these results will deepen the understanding of the THz singular beam generation mechanism and orbital angular momentum (OAM) conversion in laser induced gas-filamentation.