A vertex strong geodetic set S of x of G is called a total vertex strong geodetic set of G if G[S] has no isolated vertex. The minimum cardinality of a total vertex strong geodetic set of G is called the total vertex strong geodetic number of G and is denoted by tsg_x (G). Any total vertex strong geodetic set of cardinality tsg_x (G) is called a tsg_x-set of G. Some of the standard graphs are determined. Necessary conditions for tsg_x (G) to be n or n-1 are given for some vertex x in G. It is shown for every pair of integers a and b with 2≤ a≤b, there exists a connected graph G such that〖 sg〗_x (G)=a and t〖sg〗_x (G)=b for some vertex x in G, where 〖 sg〗_x (G) is the vertex strong geodetic number of x of G