In　this　paper,　the　minimum　variance　distortionless　response　(MVDR)　beamforming　technique　is　studied　in　the　presence　of　a　spatially　coherently　distributed　(CD)　source.　In　the　first　part,　we　propose　the　CD-MVDR　beamforming　in　which　the　steering　vector　of　the　CD　source　model　is　used　instead　of　the　conventional　point　source　model.　We　derive　a　theoretical　expression　of　the　white　noise　gain　of　CD-MVDR　beamforming,　which　is　inversely　proportional　to　the　square　of　the　difference　between　the　angular　dispersion　of　the　actual　source　and　that　of　the　CD-MVDR　beamforming　model.　In　the　second　part,　based　on　the　performance　analyses,　we　propose　an　efficient　optimization　method　for　the　microphone　array　geometry　to　reduce　the　impact　of　the　CD　source　angular　dispersion　on　the　performance　of　the　conventional　MVDR　beamforming.　Simulation　results　validate　our　proposed　theoretical　expressions　and　show　that　with　the　proposed　geometry,　the　conventional　MVDR　beamforming　tends　to　be　significantly　more　robust　to　the　angular　dispersion　of　the　CD　source　for　both　white　noise　gain　(WNG)　and　directivity　factor　(DF).　©　2023,　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.