The blade tip-timing (BTT) method has become the industry standard in blade vibration measurement. It monitors blade vibration based on the different times of arrival (ToAs) between blade vibration and not. The optical fiber bundle (OFB) probe is widely used to obtain ToA because of its small size, fast response, and high tip-timing accuracy. ToA is usually obtained by comparing the received signal with a fixed threshold level. However, the varying blade tip clearance (BTC) will affect the received signal, which directly causes the tip-timing error. We propose an optical fiber probe with GRIN lens, which eliminates the tip-timing error caused by varying BTC through the constant-fraction discrimination (CFD) method. The model of the OFB probe with GRIN lens is first established. Model analysis indicates that ToA obtained by the proposed method is constant no matter how BTC changes. Finally, the accuracy of the model and the effectiveness of the method are verified by two experiments. When BTC varied from 1.5 to 3.5 mm, the maximum tip-timing errors of OFB probe without and with GRIN lens were 181.12  μs and 10.44  μs, respectively.