We have calculated the spectroscopic data of the odd series nd [1/2]1 (3 ≤ n ≤ 9) of neutral argon atom relative to the ground level 3P⁶ ¹S₀ using a fully relativistic approach based on the Dirac equation. This series is one of three intermediate Rydberg series that converge to the first limit of ionization. The energy levels of this series are predicted. The obtained energy levels results are judged by comparing them with the experimental ones available in the literature. Within the uncertainty in the theoretical results, the agreement between our results and the experimental ones was found to be reasonable. Based on this agreement, the oscillator strengths f_{ij}, the radiative transition rates A_{ij}, the Landé g-factor, the magnetic dipole moment and the electric quadrupole hyperfine constants for the levels in question are calculated. The obtained results of f_{ij}, A_{ij}, and Landé g-factor are compared with the theoretical and experimental results published by other researchers where available as well as those published by NIST. Within the uncertainty in our results, a good agreement is found. Moreover, the studied levels are situated near and under the first limit of ionization where autoionization effects take place.