The graded-index optical transmission medium with a low transmission loss, a favorable index distribution and superior in softness etc. can be constituted by a mixture of polymers Pn having different refractive indices and by restricting the attenuation L.sub.F of the medium in accordance with the below inequality (I).The medium may advantageously be produced by way of admixing a thermoplastic polymer (A) and a monomer (B) able to form a polymer mutually soluble with the polymer (A), molding the mixture and volatilizing the monomer (B) from the surface of thus shaped substance. ##EQU1## wherein Wn are the respective proportions by weight of mixing of the polymers Pn to the whole of the mixture of the polymers Pn, and ##EQU2## Wn is equal to one.