An interrogation technique for fiber Bragg grating (FBG) strain sensors with dynamic temperature compensation using a single-multiple-single-mode (SMS) fiber filter as a temperature compensating element is presented. Experimental results show that this technique offers a resolution of better than $3.4\mathrm{\mu \epsilon }$ for strain measurements in the range from 0 to $1667\mathrm{\mu \epsilon }$ , and the temperature induced error is as low as $34\mathrm{\mu \epsilon }$ in the temperature range from 10 to $60°\mathrm{C}$ . The temperature induced error could be further reduced if the temperature sensitivity (the rate of temperature induced wavelength shift) of the SMS filter was closer to that of the FBG sensor. This can be achieved by selecting a multimode fiber for the SMS filter with appropriate parameters. The proposed technique can be modified for simultaneous measurements of strain and temperature with an experimentally achieved resolution of better than $1°\mathrm{C}$ .