Variable thickness composite laminates (VTCL) are susceptible to impact during use and may result in irreparable internal damage. In order to locate the internal impact damage of complex composite structures and monitor the impact signals of VTCL at the same time, a low velocity impact (LVI) monitoring system based on an optical fiber sensing network was constructed. Fiber Bragg grating (FBG) sensors are suitable for monitoring strain characteristics. By arranging FBG sensors on the laminate, we studied the spectrum analysis and localization of the impact signal collected by a FBG demodulator at constant temperature. The prior knowledge of variable thickness composite structures is difficult to obtain, and the multi-sensor dynamic monitoring is complex and difficult to realize. In order to locate the LVI of composite structures without prior knowledge, based on empirical mode decomposition (EMD), we proposed an impact localization method with zero-mean normalized cross-correlation (ZNCC) and thickness correction. The experimental results of LVI localization verification show that the ZNCC algorithm can effectively remove the temperature cross-sensitivity and impact energy influencing factors, and the thickness correction can reduce the interference of variable thickness characteristics on localization performance. The maximum localization error is 24.41 mm and the average error is 15.67 mm, which meets engineering application requirements. The method of variable-thickness normalization significantly improves impact localization performance for VTCL.