Based on the effect of edge-filter, it is for the first time that a novel long-period fiber grating is used as sensor to measure static and dynamic strain. The input signal from a light source of single wavelength is attenuated by the long-period fiber grating, and then received by a photodetector. The loss band of the LPFG will shift in the direction to shorter wavelength when the grating is strained. Due to the effect of edge-filter, the light intensity received by the photodetector will change in response. As a result, the electrical output of the photodetector can be used to reflect the strain forced on the grating. In the static measurement, the result shows that the relation between the electrical output of the sensor and the strain forms a conic. The resolution of this sensing system is better than 10 με, and the error is about ±10 με. This system can response dynamic strain over 5 kHz too. This sensor system is low-cost and fast.