Abstract: Let G =（V（G）,E（G）） be a connected graph of order n,V（G） be vertex set of G,E（G） be edge set of G,deg（x） be degree of the vertex x.The inverse symmetric division deg index of G is ISDD（G）=∑_{xy∈E（G）}（deg（x）·deg（y）/deg（x）~2+deg（y）~2）.Inequality and classification discussion are used to study the ISDD（G） of molecular tree with fixed number of pendent vertices,respectively,the extreme value of the ISDD index of the molecular tree with the number of pendent vertices is even number and the number of pendent vertices is more than or equal to 3 are discussed,the tree whose vertex degree is less than 4 is called molecular tree.Firstly,the minimum value of the inverse symmetric division deg index of G is determined when the number of pendent vertices is even,that is ISDD（MT） =1/2n-31/85p-1/10.Secondly,when the number of pendent vertices is greater than or equal to 3,the maximum value of the inverse symmetric division deg index of G in the molecular tree is determined,that is ISDD（MT） =1/2n-9/65p-1/2,and the molecular tree of ISDD index reaching the extreme value is described.