A lapping tape has an abrasive coat which comprises an acicular iron oxide powder having a surface area of at least 30 m.sup.2 /g as determined by the BET method and a granular inorganic powder having a Moh's hardness of more than 7 and contained in an amount of from 2.0 to 30 percent by weight on the basis of the weight of the oxide powder. The coat has a centerline mean roughness between 0.015 and 0.03 .mu.m. Preferably the acicular iron oxide is magnetic, and the inorganic powder ranges in particle diameter from 0.05 to 0.4 .mu.m.