A two-phase flow configuration in which the gas phase flows upwards while the liquid phase flows downwards is referred to as a counter-current flow pattern. This flow configuration cannot be preserved if any flow rate exceeds a criterion known as the counter-current flow limitation (CCFL) or flooding. Since the CCFL is important to chemical engineers, it has long been studied via experimental and analytical approaches. Most of the previous CCFL experiments in annular channels have been carried out with a small diameter annulus and large gap-to-diameter ratio annulus. The present experiment examines the CCFL in narrow annular channels having gap sizes of 1, 2, 3, and 5 mm. The outer diameter of the annular passage is 500 mm. At a gap size of 1 mm, it was visually observed that a CCFL locally occurred in some region of the periphery while the other region remained in a counter-current flow configuration. The region under partial CCFL condition expanded with an increase in the air flow rate, finally reaching a global CCFL. The air flow rate for the global CCFL was roughly 15% larger than that for initiation of a partial CCFL. This difference in air flow rate between the initiation of a partial CCFL and the global CCFL was reduced as the gap size increased. When the gap size was 5 mm, the partial CCFL was not observed, but onset of flooding led to a global CCFL. Because of the existence of a transient period, the CCFL was experimentally defined as the situation where net water accumulation is sustained. The measured CCFL data are presented in the form of a Wallis’ type correlation. Two length scales, hydraulic diameter and average circumference, were examined as the characteristic length scale. The average circumference appeared to better fit the experimental data, including results reported elsewhere. A new correlation using the average circumference as the characteristic length scale is suggested based on the experimental measurements of the present work and previous reports.