Traditional fiber strain sensing technologies can not meet the properties of high precision, good environment adaptability and realize dynamic strain sensing stably at the same time. In order to solve this problem, an optical interference principle was adopted to realize optical fiber strain sensing in this paper, a kind of high-precision dynamic optical fiber strain sensing system with a good environment adaptability based on an interference structure was designed. The system can be used to detect strain stably based on cross correlation coefficient of swept interferometer signal. This paper also proposes the dynamic detecting method that significantly increases practical detection range to overcome the drawback that the system can only detect small strain and realize strain sensing dynamicly. The cubic spline interpolation algorithm was used to improve the accuracy of detection of small strain. Theoretical analysis and simulation experiments show that, the precision of measurements after interpolation is 2.3 times which is higher than that before interpolation, and the maximum measurement error of strain is only 9 nε when the signal to noise ratio is 15 dB.