Carbon fiber precursor fiber bundle, thermally-stabilized fiber bundle, production method thereof, and method for producing carbon fiber bundle

A method for producing a carbon fiber precursor fiber bundle, comprising:

• subjecting a fiber bundle composed of acrylamide-based polymer fibers to a drawing process at a draw ratio of 1.3 to 100 at a temperature in a range of 225 to 320° C., to obtain the carbon fiber precursor fiber bundle of the acrylamide-based polymer fibers, wherein
• the acrylamide-based polymer is selected from the group consisting of a homopolymer of an acrylamide-based monomer and a copolymer of 50 mol % or more of an acrylamide-based monomer and 50 mol % or less of an additional polymerizable monomer;
• and
• the carbon fiber precursor fiber bundle contains single fibers having a circular cross section in a proportion of 30 to 100%, wherein the circular cross section has a ratio of a major axis to a minor axis of 1.0 to 1.3 in a cross section orthogonal to a longitudinal direction of the single fiber, and a fineness of the single fiber is 0.1 to 7 dtex.