For a competitive sensor, both the sensitivity enhancement and calibration convenience are important. However, for surface-mounted fiber grating strain sensors, researchers in previous studies have seldom addressed these two capabilities simultaneously. Using the coupled-mode theory, we calculated the voltage signals from the filtered spectral-power interrogation system for a fiber Bragg grating with a glued grating or with a glue-free grating subject to different strain fields. Under a grating zone (the targeted surface), a one-dimensional linearly varied strain field, described by both the parameters of the average strain and the strain gradient, was considered. Finally, a simple and easy formula is provided (the improved-bonding linearly chirped fiber grating) to achieve both the sensitivity enhancement and calibration convenience at the same time for the strain sensor.