The inverse SturmLiouville problem on a finite interval with separated boundaryvalue conditions is considered. Through analysing the asymptoticity of eigenvalues and the nodes of eigenfunction， give conditions that density function and potential function can be uniquely determined by the nodes.It is proved that density function can be uniquely determined up to a multiplicative constant by a dense subset of nodal positions when the potential function is given; and the potential function can be uniquely determined by the same nodal positions of systems when the density function is given.

SturmLiouville problem; inverse nodal problem; density function; potential function