In order to improve the temperature and strain sensitivity of fiber Bragg grating (FBG),we propose a FBGs array fiber sensor based on Vernier-effect.The proposed sensor is composed of Lyot interferometer (LI) and FBGs array.LI is the reference interferometer of Vernier-effect,and FBGs array with the same reflectivity and wavelength interval is the sensing part of Vernier-effect.The Vernier-effect is caused by the small difference between the equal wavelength interval of the FBGs array and the FSR of the LI.LI consists of two polarizers and a section of panda polarization maintaining fiber (PMF).The simulation results show that there is a Vernier-effect between LI and FBGs array.The temperature and strain response of the sensor with different FSR of the LI were studied.When the FSR of LI is 1.76 nm,the temperature sensitivity and strain sensitivity of the proposed sensor are -241.60 pm/℃ and -13.42pm/℃ respectively.The most outstanding advantage of the hybrid cascade structure is that it can easily change the temperature sensitivity and strain sensitivity of the proposed FBG sensor by changing the FSR of the LI or the wavelength interval of the FBGs array.This sensor provides a new way to improve the sensing ability of FBG.