Let G(V, E) be a simple graph,k is a positive integer.f is a mapping from V (G) ∪ E(G) to {1, 2, ··· ,k } such that ∀uv ∈ E(G),then f (u) �= f (v); ∀uv, vw ∈ E(G) ,u �= w, f(uv) �= f (vw); ∀uv ∈ E(G) ,C (u) �= C(v),we say that f is the incidence-adjacent vertex distinguishing total coloring of G.The minimum number of k is called the incidence-adjacent vertex distinguishing total chromatic number of G.Where C(u )= {f (u) }∪{ f (uv)|uv ∈ E(G)}. In this paper, we discuss some graphs whose incidenceadjacent vertex distinguishing total chromatic number is just Δ,Δ+1,Δ+2, and present a conjecture that the incidenceadjacent vertex distinguishing total chromatic number of a graph is no more than Δ +2 .