In this paper we study the initial boundary value problem of GBBM equations on unbounded domain ut - △ut = divf(u)u(x, 0) = u0(x)and corresponding Cauchy problem. Under the conditions: f(s) ∈ C1 and satisfies u0(x) ∈ W2,p(Ω) ∩ W2,2(Ω) ∩ W01,p(Ω)(W2,p(Rn) ∩ W2,2(Rn) for Cauchy problem),2 ≤ p <∞, we obtain the existence and uniqueness of global solution u(x,t) ∈W1,∞ (0, T; W2,p (Ω)∩W2,2 (Ω)∩W1,p0(Ω)) ( W1,∞ (0, T; W2,p(Rn)∩W2.2 (Rn)) for Cauchy problem), so the results of [1] and [2] are generalized and improved in essential.