A practically fast electroless copper plating solution is provided by adding a specific monoamine as an accelerator. The accelerator should be a tertiary monoamine and cannot be a diamine, does not have a complexing ability for copper ion, and does not contain a ketone or carboxyl group or an unsaturated group. Specific examples of such monoamines include triethylamine, tripropylamine, tribenzylamine, N-methylpiperidine, and diethylaminoethanol.