A　large-scale　fully　digital　receive　antenna　array　can　provide　very　high-resolution　direction　of　arrival　(DOA)　estimation,　but　resulting　in　a　significantly　high　RF-chain　circuit　cost.　Thus,　a　hybrid　analog　and　digital　(HAD)　structure　is　preferred.　Two　phase　alignment　(PA)　methods,　HAD　PA　(HADPA)　and　hybrid　digital　and　analog　PA　(HDAPA),　are　proposed　to　estimate　DOA　based　on　the　parametric　method.　Compared　to　analog　PA　(APA),　they　can　significantly　reduce　the　complexity　in　the　PA　phases.　Subsequently,　a　fast　root　multiple　signal　classification　HDAPA　(root-MUSIC-HDAPA)　method　is　proposed　specially　for　this　hybrid　structure　to　implement　an　approximately　analytical　solution.　Due　to　the　HAD　structure,　there　exists　the　effect　of　direction-finding　ambiguity.　A　smart　strategy　of　maximizing　the　average　receive　power　is　adopted　to　delete　those　spurious　solutions　and　preserve　the　true　optimal　solution　by　linear　searching　over　a　set　of　limited　finite　candidate　directions.　This　results　in　a　significant　reduction　in　computational　complexity.　Eventually,　the　Cramer-Rao　lower　bound　(CRLB)　of　finding　emitter　direction　using　the　HAD　structure　is　derived.　Simulation　results　show　that　our　proposed　methods,　root-MUSIC-HDAPA　and　HDAPA,　can　achieve　the　hybrid　CRLB　with　their　complexities　being　significantly　lower　than　those　of　pure　linear　searching-based　methods,　such　as　APA.