In this paper, we deal with the existence of global mild solutions and asymptotic behavior to the viscous Camassa–Holm equation in the locally uniform spaces. First we establish the global well-posedness for the Cauchy problem of viscous Camassa–Holm equation in $${\mathbb {R}}^1$$ for any initial data $$u_0\in {\dot{H}}^1_U({\mathbb {R}}^1).$$ Then we study the long time dynamical behavior of non-autonomous viscous Camassa–Holm equation on $${\mathbb {R}}^1$$ with a new class of external forces and show the existence of $$(H^1_U({\mathbb {R}}^1),H^1_\phi ({\mathbb {R}}^1))$$ -uniform(w.r.t. $$g\in \mathcal {H}_{L^2_U({\mathbb {R}}^1)}(g_0)$$ ) attractor $$\mathcal {A}_{\mathcal {H}_{L^2_U({\mathbb {R}}^1)}(g_0)}$$ with locally uniform external forces being translation uniform bounded but not translation compact in $$L_b^2({\mathbb {R}};L^2_U({\mathbb {R}}^1))$$ .