This invention relates to an antimicrobial composition, especially one which provides synergistic anti-dandruff efficacy. This is achieved through a judicious combination of anti-dandruff agent zinc pyrithione and select antimicrobial lipids. These compositions can be delivered through shampoo or conditioner. Disclosed is an anti-microbial composition comprising: (i) 0.1 to 3% by weight of zinc pyrithione; (ii) 0.01 to 5.0% by weight of an antimicrobial lipid selected from sapienic acid, palmitoleic acid, sphingosine, dihydrosphingosine, and phytosphingosine; and a cosmetically acceptable vehicle, wherein said composition is a shampoo or a conditioner for preventing or alleviating the symptoms of dandruff on the scalp and/or hair and where an antimicrobial alcohol having 1 to 7 carbon atoms are absent from the composition.