A　narrow-linewidth　ytterbium　(Yb)-doped　phosphate　fiber　laser　based　on　fiber　Bragg　grating　(FBG)　operating　around　980　nm　is　reported.　Two　different　kinds　of　cavity　are　applied　to　obtain　the　980　nm　narrow-linewidth　output.　One　kind　of　the　cavity　consists　of　a　0.35　nm　broadband　lindwidth　high-reflection　FBG　and　the　Yb-doped　phosphate　fiber　end　with　0　degrees　angle,　which　generates　a　maximum　output　power　of　25　mW.　The　other　kind　of　resonator　is　composed　of　a　single　mode　Yb-doped　phosphate　fiber　and　a　pair　of　FBGs.　Over　10.7　mW　stable　continuous　wave　are　obtained　with　two　longitudinal　modes　at　980　nm.　We　have　given　a　detailed　analysis　and　discussion　for　the　results.