Children with attention-deficit/hyperactivity disorder show deficits in processing speed, as well as aberrant neural oscillations, including both periodic (oscillatory) and aperiodic (1/f-like) activity, reflecting the pattern of power across frequencies. Both components were suggested as underlying neural mechanisms of cognitive dysfunctions in attention-deficit/hyperactivity disorder. Here, we examined differences in processing speed and resting-state-Electroencephalogram neural oscillations and their associations between 6- and 12-year-old children with (n = 33) and without (n = 33) attention-deficit/hyperactivity disorder. Spectral analyses of the resting-state EEG signal using fast Fourier transform revealed increased power in fronto-central theta and beta oscillations for the attention-deficit/hyperactivity disorder group, but no differences in the theta/beta ratio. Using the parameterization method, we found a higher aperiodic exponent, which has been suggested to reflect lower neuronal excitation-inhibition, in the attention-deficit/hyperactivity disorder group. While fast Fourier transform-based theta power correlated with clinical symptoms for the attention-deficit/hyperactivity disorder group only, the aperiodic exponent was negatively correlated with processing speed across the entire sample. Finally, the aperiodic exponent was correlated with fast Fourier transform-based beta power. These results highlight the different and complementary contribution of periodic and aperiodic components of the neural spectrum as metrics for evaluation of processing speed in attention-deficit/hyperactivity disorder. Future studies should further clarify the roles of periodic and aperiodic components in additional cognitive functions and in relation to clinical status.