Li-like ions widely exist in astrophysical and laboratory plasmas, and their precise atomic parameters (e.g. excitation energies and transition rates) are very important for plasma diagnostics and spectral analysis. In this work, we employ the GRASP2018 software package, which is widely used in atomic structure calculations, to systematically compute the lowest 15 energy levels and the electric dipole (E1), magnetic dipole (M1), and electric quadrupole (E2) transition rates between them of 17 Li-like ions across the isoelectronic sequence (Z = 6–51: C³⁺, F⁶⁺, Mg⁹⁺, P¹²⁺, Ar¹⁵⁺, Sc¹⁸⁺, Cr²¹⁺, Co²⁴⁺, Zn²⁷⁺, As³⁰⁺, Kr³³⁺, Y³⁶⁺, Mo³⁹⁺, Rh⁴²⁺, Cd⁴⁵⁺, Sn³⁷⁺, Sb³⁸⁺). The calculations are based on the multi-configuration Dirac-Fock (MCDF) and configuration interaction (CI) method combined with high-order relativistic corrections and quantum electrodynamics effects such as Breit interaction, self-energy correction and vacuum polarization. The computational convergence is achieved. The calculated excitation energies and transition rates are compared with the NIST database and previous theoretical results. Due to the reasonable construction and larger scale of baseset, the current computational results show evident improvement compared with the results obtained using the same MCDF+CI method previously. Particularly for the two lowest excited states, [1s²2p]_1/2 and [1s²2p]_3/2, which exhibit slower convergence, the relative difference between current results and the NIST data is reduced by one to two orders of magnitude compared with previous MCDF+CI calculations. This accuracy even approaches that achieved by S-matrix methods specifically optimized for the ground state and these two lowest excited states. For transition rates, except for certain weak transitions with rates below $ {10}^{3}\;{{{\mathrm{s}}}}^{{-1}} $, the difference between our calculations and previous theoretical results obtained using the MCDF+CI method is still within 1%. Furthermore, our calculations accord with the NIST data within 5% for the majority of transitions. A comparison of NIST data with other previous theoretical results shows evident discrepancies between our calculations and the NIST data for some excitation energies and transition rates. Our results are consistent with other theoretical results for these specific values, indicating that these particular energy levels and transitions need more detailed theoretical and experimental investigation. This work provides highly accurate data for supporting experimental diagnostics and theoretical modeling of astrophysical and laboratory plasmas in future research. The datasets presented in this paper are openly available at https://www.doi.org/10.57760/sciencedb.j00213.00154.