A method for manufacturing a resin-coated metal sheet comprising: laminating two or more kinds of molten resins, to form a multilayer film; extruding the multilayer film through a multi-manifold die onto a metal sheet; wherein at least one kind of molten resin contains a coloring component; wherein said molten resins include a first resin having a high melt viscosity and a second resin having a low melt viscosity; wherein the multi-manifold die has plural resin passages through which plural resins pass; wherein the resin passage through which the first resin passes is maintained at a higher temperature than the resin passage through which the low melt viscosity resin passes; wherein the difference in melt viscosity of adjoining resin layers is 3,000 poises or less at a shear rate of 20 to 500 s−1; wherein the molten resin containing a coloring component has a melt tension Tm in the range of 0.5 g≧1.0 g, and a thickness of the layer of the resin containing a coloring component is equal to one-third or more of the total thickness of the resin coating.