During the propagation of waves from deep sea to nearshore， reflection and transmission occur due to changes in water depth and complex topography. In particular， when the seabed topography exhibits periodic variations， the well-known wave Bragg resonance phenomenon emerges. Based on the modified mild-slope equation， this paper established a corresponding finite-difference numerical model to investigate the effects of cross-sectional topography of a coral reef profile on wave reflection and transmission. First， the model was validated by simulating wave reflection over a periodically undulating trapezoidal topography on a horizontal seabed. The numerical results showed good agreement with existing analytical solutions， confirming the reliability of the model. Subsequently， the systematic analysis was conducted to examine the effects of the relative lagoon depth （lagoon depth relative to the water depth in the study area， h₁/h₀） and the relative excavation pit depth （excavation pit depth relative to the water depth in the study area， h_p/h₀） on the coefficients of wave reflection and transmission. The results indicate that as h₁/h₀ increases， the reflection coefficient corresponding to wave resonance increases significantly， while the transmission coefficient gradually decreases. Moreover， the bandwidth of the resonance band widens， and the resonance frequencies of both reflected and transmitted waves shift downward. In contrast， with an increase in h_p/h₀， the reflection coefficient at resonance decreases slightly， while the transmission coefficient shows a certain increasing trend. Additionally， as h_p/h₀ increases from 3/7 to 5/7， the resonance frequencies of both reflected and transmitted waves shift upward.