In a graded index optical fiber whose refractive index distribution (n) at the radial length r is given by ##EQU1## where (n.sub.0) is the refractive index at the core axis, (a) is the core radius, .alpha. is a power exponent, n.sub.e is the refractive index of the cladding, and .DELTA.=(n.sub.0 -n.sub.e)/n.sub.0, said exponent .alpha. and the normalized frequency v (=(2.pi.an.sub.0 /.lambda.).sqroot.2.DELTA., .lambda. is the wavelength) are determined so that the group delay of the fundamental mode is equal to that of the first higher order mode. In particular, the value of .alpha. is determined in the range 3.2.ltoreq..alpha..ltoreq.6.0. Thus, the optical fiber with both a broad bandwidth and a large core diameter can be provided. A large core diameter optical fiber facilitates the connection or the splicing of two optical fibers.