An edge-to-vertex Steiner set ???? of a connected graph ???? is called a total edge-tovertex Steiner set if has no isolated edges. The minimum cardinality of a total edge-to-vertex Steiner set of ???? is a total edge-to-vertex Steinernumber and is denoted by ???????????????? (????).Some general properties satisfied by this concept are studied. Some of the standard graphs are determined.If ????, ???? and ???? are positive integers such that 4 ≤ ???? ≤ ???? then there exists a connected graph ???? such that ???????????? (????) = ???? and ????????????????(????) = ????,where ???????????? (????)is aedge-to-vertex Steiner number of a graph.