In this paper, we propose a novel strategy for a snake robot to move straight up a cylindrical surface. Prior works on pole-climbing for a snake robot mainly utilized a rolling helix gait, and although proven to be efficient, it does not reassemble movements made by a natural snake. We take inspiration from nature and seek to imitate the Arboreal Concertina Locomotion (ACL) from real-life serpents. In order to represent the 3D curves that make up the key motion patterns of ACL, we establish a set of parametric equations that identify periodic functions, which produce a sequence of backbone curves. We then build up the gait equation using the curvature integration method, and finally, we propose a simple motion estimation strategy using virtual chassis and non-slip model assumptions. We present experimental results using a 20-DOF snake robot traversing outside of a straight pipe.