In music, chords are organized into hierarchical structures based on recursive or embedded syntax. How the brain extracts recursive grammar is a central question in musical cognition and other cognitive neuroscience, but the precise mechanism remains unclear. By analyzing event related potentials (ERPs) and neural oscillatory activity, the present study investigated neurocognitive mechanisms underlying the processing of center-embedded structure in music by examining the differences in center-embedded and non-embedded structure processing and evaluating how these differences are affected by musical proficiency. Based on Western musical proficiency, the subjects were divided into two groups, non-experts and experts. The results revealed that for non-experts, the processing of center-embedded structure elicited greater early right-anterior negativity (ERAN) and N5 components as well as, reduced alpha and gamma activities than did the non-embedded structure. For experts, no significant difference in the ERP response was observed between the processing of non-embedded and center-embedded structures; however, the processing of center-embedded structure elicited increased beta activity compared to non-embedded structure. These findings indicate that listeners different in proficiency would rely on different cognitive neural mechanisms in music processing with the syntactic complexity increases.