Electrical generation of THz spin waves is theoretically explored in an antiferromangetic nanostrip via the current-induced spin-orbit torque. The analysis based on micromagnetic simulations clearly illustrates that the Neel-vector oscillations excited at one end of the magnetic strip can propagate in the form of a traveling wave when the nanostrip axis aligns with the magnetic easy-axis. A sizable threshold is observed in the driving current density or the torque to overcome the unfavorable anisotropy as expected. The generated spin waves are found to travel over a long distance while the angle of rotation undergoes continuous decay in the presence of non-zero damping. The oscillation frequency is tunable via the strength of the spin-orbit torque, reaching the THz regime. Other key characteristics of the spin waves such as the phase and the chirality can also be modulated actively. The simulation results further indicate the possibility of wave-like superposition between the excited spin oscillations, illustrating its application as an efficient source of spin-wave signals for information processing.