Working memory capacity (WMC) can predict conflict control ability. Measures of both abilities are impaired by anxiety, which is often inversely linked with mindfulness. It has been shown that a combination of high mindfulness and low anxiety is associated with better conflict control and WMC. The current study explored the electrophysiology related to such behavioral differences. Two experimental groups, one with high mindfulness and low anxiety (HMLA) and one with low mindfulness and high anxiety (LMHA), performed a color Stroop task and a change detection task, both with simultaneous electroencephalogram (EEG) recording. An advanced EEG analytical approach, Hilbert–Huang transform (HHT) analysis, was employed. This is regarded as a robust method to analyze non-linear and non-stationary signals. Lower delta activity at posterior temporal and occipital regions was seen in the HMLA group for the Stroop conflict conditions and might be generally associated with higher accuracy in this group and indicative of higher attentiveness. Higher accuracy rates and WMC were seen in the HMLA group and might be specifically associated with the higher alpha activity observed in prefrontal cortex, fronto-central and centro-parietal regions in this group. Future studies should explore how mindfulness and anxiety can independently affect these cognitive functions and their associated neurophysiology.