Personality traits must relate to stable neural processes, yet few robust neural correlates of personality have been discovered. Recent methodological advances enable measurement of cortical travelling waves, which likely underpin information flow between brain regions. Here, we explore whether cortical travelling waves relate to personality traits from the "Big Five" taxonomy. We assessed personality traits and recorded resting electroencephalography (EEG) from 300 participants. We computed travelling wave strength using a 3D fast Fourier transform and explored relationships between alpha travelling waves and personality traits. Trait Agreeableness and Openness/Intellect had significant relationships to travelling waves that passed multiple-comparison controls ( = 0.019 and = 0.036 respectively). Agreeableness related to interhemispheric waves travelling from the right hemisphere along central lines (rho = 0.263, < 0.001, = 356.350). This relationship was unique to the compassion aspect (t = 3.719, < 0.001) rather than politeness aspect of Agreeableness (t = 0.897, = 0.370). Openness/Intellect related to backwards travelling waves along midline electrodes (rho = 0.197, < 0.001, = 13.800), which was confirmed for the Openness aspect (rho = 0.216, < 0.001, = 26.444) but not the Intellect aspect (rho = 0.093, = 0.109, = 0.344). Greater cortical travelling wave strength from right temporal regions was associated with higher trait compassion, and backwards travelling wave strength along midline electrodes was associated with trait openness. Further research is needed to investigate the mechanistic role of travelling waves in personality traits and other individual differences.