PURPOSE: To obtain the titled carbon yarn industrially, readily and inexpensively, by subjecting a novolak polymer to melt spinning, thermally curing and carbonizing in a nonoxidizing atmosphere while applying tension to the yarn in the yarn direction.

CONSTITUTION: A 3,5-alkylphenol is reacted with an aldehyde such as formalin or trioxane in the presence of an acid catalyst to give a novolak polymer. Then the novolak polymer is washed with water, dried, subjected to melt spinning and further thermally cured with a mixed aqueous solution of an acidic catalyst and an aldehyde to give novolak polymer yarn. Then the novolak polymer yarn is carbonized in a nonoxidizing atmosphere such as nitrogen or argon while applying tension to the yarn in the yarn direction and optionally graphitized while applying tension to give the aimed carbon yarn.