The vortex-induced vibration (VIV) of a cylinder is a typical fluid-solid coupling problem. Previous investigations on VIV responses were mainly made under increasing-velocity flow and wall-free conditions. Nevertheless, the natural flow always features with alternately increasing or decreasing velocities, so that the VIV response of a near-wall cylinder holds different characteristics from that of a wall-free cylinder. In this study, a VIV device for a cylinder with low structural damping was designed and constructed in conjunction with a flume. Based on dimensional analyses, a series of flume model tests were carried out to investigate the critical velocities for the initiation and the cease of VIV (i.e., the upper critical and lower critical reduced velocities) of a near-wall cylinder under the action of increasing-velocity and decreasing-velocity flows, respectively. To examine wall-proximity effects on the VIV hysteresis, synchronous measurements were made for the time-variation of vibration displacement and the corresponding flow fields around the cylinder. Meanwhile, a specially designed PIV system with bottom-up laser scanning was employed to capture the flow field characteristics. Experimental observations indicate that the critical velocity for the initiation of VIV of a near-wall cylinder decreases with the decrease of gap-to-diameter ratio. The lower-critical reduced velocity for the cease of VIV under decreasing-velocity conditions is however much smaller than the upper-critical value for the initiation of VIV under increasing-velocity conditions. The deviation of the upper-critical reduced velocity from the lower-critical one is used for quantitative characterization of the hysteresis in VIVs, which increases approximately linearly with the decrease of gap-to-diameter ratio. Moreover, it was found that such VIV hysteresis is always accompanied with the jump of vibration amplitude, whose value decreases nonlinearly with the decrease of gap-to-diameter ratio.