The Drazin inverse of a lower Hessenberg matrix is considered. If $A$ is a singular lower Hessenberg matrix and $a_{i,i+1}=\neq 0,i=1,2,\cdots,n-1$, then $A^D$ can be given, and expressed explicitly by elements of $A$. The structure of the Drazin inverse of a lower Hessenberg matrix is also studied.