The present paper explores the terahertz (THz) generation by the interaction of obliquely incident laser beams with the array of vertically aligned anharmonic carbon nanotubes (CNTs) acting as dipole antennas. In the scheme, anharmonicity arises due to the nonlinear variation of restoration force on the various electrons of CNTs and it plays a key role in the enhancement of THz generation. The anharmonic CNTs help in broadening the resonance peak, which paves the way for the enhancement of the normalized THz amplitude. The laser beams incident obliquely on the close-packed array of vertically aligned anharmonic CNTs grown over the glass substrate and set oscillations in the CNTs so that each CNT act as the oscillatory dipole to generate THz radiation. The THz electric field shows enhancement at surface plasmon resonance frequency , where is the characteristic parameter of CNTs, is the relative permittivity of lattice and is the plasma frequency. This scheme is quite suitable to generate THz radiations in the milliwatt range of optimized values of the laser and CNTs parameters. We also explore the impact of polarization, S-parameter, critical angle, and length-matching effects of CNT antennas on the THz generation.