We present the results of BV time-series photometry of the globular cluster NGC 288. Ob- servations were carried out to search for variable stars using the Korea Microlensing Telescope Network (KMTNet) 1.6-m telescopes and a 4k pre-science CCD camera during a test observation from August to December, 2014. We found a new SX Phe star and confirmed twelve previously known variable stars in NGC 288. For the semi-regular variable star V1, we newly determined a period of 37.3 days from light curves spanning 137 days. The light-curve solution of the eclipsing binary V10 indicates that the system is probably a detached system. The pulsation properties of nine SX Phe stars were examined by applying multiple frequency analysis to their light curves. We derived a new Period-Luminosity (P-L) relation, hMV i = −2.476(±0.300) logP − 0.354(±0.385), from six SX Phe stars showing the fundamental mode. Additionally, the period ratios of three SX Phe stars that probably have a double-radial mode were investigated; PFO/PF = 0.779 for V5, PTO/PFO = 0.685 for V9, PSO/PFO = 0.811 for V11. This paper is the first contribution in a series assessing the detections and properties of variable stars in six southern globular clusters with the KMTNet system.