Even though current microlensing follow-up observations focus on high-magnification events due to the high efficiency of planet detection, it is very difficult to do a confident detection of planets in high-magnification events with extremely weak central perturbations (i.e., the fractional deviation is ${delta}{leq}0.02$). For the confident detection of planets in the extremely weak central perturbation events, it is needed both the high cadence monitoring and the high photometric accuracy. A next-generation ground-based observation project, KMTNet (Korea Microlensing Telescope Network), satisfies both the conditions. Here we investigate how well planets in high-magnification events with extremely weak central perturbations are detected by KMTNet. First, we determine the probability of occurrence of events with ${delta}{leq}0.02$. From this, we find that for ${leq}100M_E$ planets in the separation of $0.2AU{leq}d{leq}20AU$, events with ${delta}{leq}0.02$ occur with a frequency of more than 70%, in which d is the projected planet-star separation. Second, we estimate the efficiency of detecting planetary signals in the events with ${delta}{leq}0.02$ via KMTNet. We find that for main-sequence and subgiant source stars, ${geq}1M_E$ planets can be detected more than 50% in a certain range that has the efficiency of ${geq}10%$ and changes with the planet mass.