A gap fiber Bragg grating (g-FBG) is fabricated by cutting a uniform FBG in the middle to introduce a small air gap between the two sections. Numerical and experimental investigations show that the g-FBG has the characteristics of both a phase shifted FBG and a Fizeau interferometer. The influence of the air-gap shift longitudinally or transversely with respect to the fiber central axis and temperature to g-FBG's spectrums are investigated with numerical simulation and experiments, and the mathematic models are made. Based on g-FBG's different sensitivity to gap width and temperature, a micro-gap and temperature simultaneous measurement sensor was demonstrated. And a g-FBG based tunable fiber ring laser with a narrow line-width is demonstrated.