We study the dynamics of liquid climbing in a narrow and tilting corner, inspired by recent work on liquid transportation on the peristome surface of Nepenthes alata. Considering the balance of gravity, interfacial tension, and viscous force, we derive a partial differential equation for the meniscus profile and numerically study the behavior of the solution for various tilting angles beta. We show that the liquid height h(t) at time t satisfies the same scaling law found for the vertical corner, i.e., h(t) proportional to t(1/3) for large t, but the coefficient depends on the tilting angle beta. The coefficient can be calculated approximately by the Onsager principle, and the result agrees well with that obtained by numerical calculation. Our model can be applied for a weakly curved corner and may provide guidance to the design of biomimetic surfaces for liquid transportation.