You have an image and want to create transparent background but have a fuzzy border.

Just to be sure that the image uses alpha channel, right click on the image Layer->Transparency->Add Alpha Channel

 

  1. On top menu of Gimp select Windows->Toolbox
  2. From the Toolbox select "Fuzzy Select Tool" (magic wand icon)
  3. Click on the background color so it can be selected and press Esc
  4. On top menu select Filters->Blur->Gaussian Blur