Provided are: a carbon fiber bundle which has a large value of single-fiber fineness and excellent productivity and which, despite this, contains few interlaced single fibers therein and has excellent spreadability; and precursor fibers which are suitable for use in producing the carbon fiber bundle. The precursor fibers are a carbon-fiber-precursor acrylic fiber bundle which comprises a polyacrylonitrile copolymer comprising 95-99 mol % acrylonitrile units and 1-5 mol % hydroxyalkyl (meth)acrylate units and which has a single-fiber fineness of 1.5-5.0 dtex. In the acrylic fiber bundle, the cross-section of each single fiber which is perpendicular to the fiber axis has a shape that has a roundness of 0.9 or less. The roundness is a value determined using equation (1) where S and L are the cross-sectional area and the circumferential length, respectively, of a single fiber which are obtained by examining, with an SEM, the cross-section of the single fiber which is perpendicular to the fiber axis and analyzing the obtained image. Roundness=4pS/L2  (1)