Enhancing　fiber　coupling　efficiency　of　a　diode-laser-fiber　is　critical　in　improving　the　efficiency　of　fiber　lasers　in　general.　As　a　pumped　source,　fast-axis　directivity　of　the　diode-laser　stack　impacts　strongly　on　fiber　coupling　efficiency.　We　propose　a　new　method　of　analysis　for　describing　the　dependence　of　fast-axis　beam　quality　and　fiber　coupling　efficiency　on　fast-axis　directivity.　Using　this　method,　we　obtain　in　computer　simulations　the　fast-axis　beam　quality　of　any　diode　laser　and　fiber　coupling　efficiency.　An　accuracy　of　96.3%　for　the　method　was　established　in　experiments.