A multilayer wiring substrate which is high in connection reliability is provided through process steps of forming more than one opening, such as a via-hole in a dielectric layer laminated on a substrate, and then applying uniform copper plating to a surface portion of the dielectric layer including the opening to thereby form a wiring layer. An electroless copper plating solution with at least one of mandelonitrile and triethyltetramine mixed therein is used to perform the intended electroless copper plating. An alternative process makes use of a electroless copper plating solution with chosen additive agents or “admixtures” containing at least one of mandelonitrile and triethyltetramine plus eriochrome black T along with at least one of 2,2′-bipyridyl, 1,10-phenanthroline, and 2,9-dimethyl-1,10-phenanthroline.