Motivated by the recent synthesis of penta-NiN2, a new two-dimensional (2D) planar material entirely composed of pentagons [ ACS Nano 2021, 15, 13539], we study its thermal transport properties based on first-principles calculations and solving the Boltzmann transport equation within the self-consistent phonon theory and four-phonon scattering formalism. We find that the intrinsic lattice thermal conductivity of penta-NiN2 is 11.67 W/mK at room temperature, which is reduced by 89.32% as compared to the value obtained by only considering three-phonon scattering processes. More interestingly, different from the general response of thermal conductivity to external strain in most 2D materials, an oscillatory decrease of the thermal conductivity with increasing biaxial tensile strain is observed, which can be attributed to the renormalization of vibrational frequencies and the nonmonotonic variation of phonon scattering rates. This work provides an accurate intrinsic thermal conductivity of penta-NiN2 and elucidates the effects of the strain-tuned vibrational modes and phonon band gap on the four-phonon scattering processes, shedding light on a better understanding of the physical mechanisms of thermal transport properties in 2D pentagon-based materials.