Low-noise terahertz (THz) radiation over 100 MV/cm generation by a linearly-polarized relativistic laser pulse interacting with a near-critical-density (NCD) plasma slab is studied by theory and particle-in-cell (PIC) simulations. A theoretical model is established to examine the dipole-like radiation emission. The THz radiation is attributed to the single-cycle, low-frequency surface current which is longitudinally constrained by the quasi-equilibrium established by the laser ponderomotive force and the ponderomotively-induced electrostatic force. Through theoretical analysis, the spatiotemporal characteristics, polarization property of the THz radiation, and the relation between the radiation strength with the initial parameters of driving laser and plasma are obtained, which are in good consistence with the PIC simulation results. Furthermore, it is found by PIC simulations that the generation of thermal electrons can be suppressed within the appropriate parameter regime, resulting in a clear THz radiation waveform. The appropriate parameter region is given for generating a low-noise intense THz radiation with peak strength reaching 100 MV/cm, which could find potential applications in nonlinear THz physics.