To achieve the quasi-distributed fiber grating sensing system with high spatial resolution and high measurement accuracy, the demodulation and calibration methods for the fiber grating sensing system are studied based on the time-division multiplexing technology. By combining the wavelength-division multiplexing technique with the time-division multiplexing technique, the obtained strain sensitivities of the two fiber gratings with a low reflectivity are 33.40 με/mV and 38.47 με/mV, and the non-linear error of the calibration is 2.8%. A time-division multiplexing fiber grating strain sensing system is established based on the edge filtering technique of the fiber grating spectrum. The cross-sensing demodulating algorithm of the multiplexing fiber grating strain is derived, and we test and demodulate the cross-sensing data of the two fiber gratings by experiments. The results show that the maximum error of the sensing system for a single measurement is 18 με, the relative error is less than 5% under the condition that the strain is more than 100 με, and the quoted error is less than 2% when the full scale is 600 με.