In　order　to　solve　the　problem　of　the　inaccuracy　in　predicting　pixels　at　the　boundary　of　the　block　in　H.264　intra　prediction,　a　hierarchy-based　intra　prediction　algorithm　was　presented　in　this　paper.　Because　of　the　close　dependency　of　pixels　within　marco　block,　the　predicted　pixels　within　the　same　block　were　taken　as　references　to　predict　other　pixels.　A　hierarchy-based　fast　intra　prediction　algorithm　was　presented　to　reduce　the　computational　complexity　of　intra　coding　in　H.264,　which　adopted　candidate　modes　required　for　hierarchy-based　structure　by　utilizing　characteristics　of　4　×　4　block　in　spatial　and　frequency　domain　to　reduce　the　quantity　of　modes　for　computation.　Furthermore,　the　relationship　between　4　×　4　mode　and　16　×　16　mode　was　exploited　in　fast　algorithm.　The　test　results　indicate　that　other　than　previous　fast　algorithms,　hierarchy-based　fast　algorithm　can　not　only　decrease　the　computational　complexity　in　intra　coding,　but　also,　more　important,　improve　coding　efficiency.