A large grain diameter under-layer of at least one selected from Cu, Ni or Rh, comprising large average diameter crystalline grains of 50 nm or more than 50 nm with the (100) crystal plane of the grains oriented parallel to the substrate surface, was formed on a substrate. Then, a magnetic recording layer was deposited on the under-layer. The magnetic recording medium carrying this structure showed very small magnetic crystalline grains in magnetic layer, and excellent overwrite characteristics and signal to noise ratio at high recording density.