This work presents a density functional theory (DFT)-based theoretical study on the cross-coupling reaction of alkyl carboxylic acids and nitrogen nucleophiles via dual copper and photoredox catalysis developed by MacMillan et al. [Nature, 2018, 559, 83-87]. The calculations showed the mechanistic details of three subprocesses proposed in the experimental study, including production of alkyl radicals, iridium(III) photoredox cycle, and copper(I) thermalredox cycle. It is found that alkyl radicals can be easily produced 47, from primary, secondary, or tertiary carboxylic acids through P2 iodonium activation. The energetically most favorable cross-coupling pathway involves coordination, deprotonation, single electron transfer (SET), radical addition, and reductive elimination. For the chlorinated indazole nucleophile (R1), the preferred C-N coupling product from the 1H-tautomer is attributed to its higher stability relative to the 2H-tautomer and the high barrier involved in the tautomerism from the 1H-tautomer to the 2H-tautomer. Meanwhile, in the case of heterocycle (R2), the C-N cross-coupling preferentially occurs at the indazole nitrogen rather than at the primary amide nitrogen, which is confirmed to be due to the stronger acidity of the indazole N-H unit, in comparison with the primary amide N-H unit in the indazole side chain. The theoretical results provide help for understanding the molecular mechanism and regioselectivity of the title reaction.