Fiber Bragg grating(FBG) has been widely used in many fields for temperature, stress and other parameters measurement, but it has cross-sensitivity problem with temperature and stress. A dual cladding radius fiber Bragg grating sensor was presented, the FBG was divided into two halves which have different cladding radiuses, the cladding radius of one half(FBG1) was unchanged, and the cladding radius of the other half(FBG2) was decreased from 62.5 μm to 40 μm. Experimental results show that, FBG2 and FBG1 have same temperature sensitivities which are 10.4 pm/°C, but FBG2 and FBG1 have different stress sensitivities which are 1.12 pm/ue and 3.89 pm/ue respectively, the stress sensitivity of FBG2 is higher than FBG1 nearly 3.24 times. The initial single Bragg reflection peak split into two reflection peaks which respectively sensitive to temperature and stress, the wavelength difference between these two peaks only impact on stress. Through this sensor, it can distinguish center reflection wavelength shift caused by temperature and stress. The sensor has simple structure, small size, low-cost, and simple fabrication，and it be can widely used in various fields to achieve simultaneous measurement of temperature and stress.