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The convergence performance of the fractional-order Darwinian particle swarm optimization (FO-DPSO) al-gorithm depends on the fractional-order α, and it can easily get trapped in the local optima. To overcome such shortcom-ing, an adaptive fractional-order Darwinian particle swarm optimization (AFO-DPSO) algorithm was proposed. In AFO-DPSO, both particle's position and velocity information were utilized adequately, together an adaptive acceleration coefficient control strategy and mutation processing mechanism were introduced for better convergence performance. Testing results on several well-known functions demonstrate that AFO-DPSO substantially enhances the performance in terms of convergence speed, solution accuracy and algorithm stability. Compared with PSO, HPSO, DPSO, APSO, FO-PSO, FO-DPSO and NCPSO, the global optimality of AFO-DPSO are greatly improved.