In　this　Letter,　a　generalized　fractional　sub-equation　method　is　proposed　for　solving　fractional　differential　equations　with　variable　coefficients.　Being　concise　and　straightforward,　this　method　is　applied　to　the　space-time　fractional　Gardner　equation　with　variable　coefficients.　As　a　result,　many　exact　solutions　are　obtained　including　hyperbolic　function　solutions,　trigonometric　function　solutions　and　rational　solutions.　It　is　shown　that　the　considered　method　provides　a　very　effective,　convenient　and　powerful　mathematical　tool　for　solving　many　other　fractional　differential　equations　in　mathematical　physics.　(C)　2012　Elsevier　B.V.　All　rights　reserved.