A first subject of the present invention is a composite powder having antibacterial and antifungal effect, in which a base powder, zinc oxide and/or zinc basic carbonate, and alkali metal salt are combined.In the composite powder, it is preferable that the base powder is an adsorbing site for adsorbing a specified enzyme, and a site in which zinc oxide and/or zinc basic carbonate and alkali metal salt are combined is an acting site having enzyme inhibiting or activating property.In the composite powder, it is preferable that the zeta-potential of an adsorbing site at pH to be used is a negative value, and the zeta-potential of an adsorbing site at pH 7.5 is −10 mV or lower.A second subject of the present invention is a cosmetic composition comprising the aforementioned composite powder.The composite powder can be also used as a skin roughening improving agent, a sensitive skin caring agent or a pimpled skin caring agent.