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The L-shell dielectronic and trielectronic recombinations of highly charged Mg-like gold ions (Au⁶⁷⁺) in the ground state 2<i>s</i>²2<i>p</i>⁶3<i>s</i>^2 1<i>S</i>₀ have been studied systematically. The recombination cross-sections and rate coefficients are carefully calculated for ∆<i>n</i> = 1 (2<i>s</i>/2<i>p →</i> 3<i>l</i>) transitions using a flexible atomic code based on the relativistic configuration interaction method and considering the Breit and QED corrections. Detailed resonance energies and resonance strengths are presented for the stronger resonances of the LM<i>n</i> (<i>n</i> = 3–12) series. It is found that the contributions of the trielectronic recombination to the total cross-section is about 13.75%, which cannot be neglected. For convenience of application, the plasma rate coefficients are also calculated and fitted to a semiempirical formula, and in the calculations, the contributions from the higher excited resonance groups <i>n</i> ≥ 13 are evaluated by an extrapolation method, which is about 2.93% of the total rate coefficient.