The deformation distribution of engineering structures can evaluate the health status of the bridge structures, but the traditional "point based" sensing technology has significant shortcomings in obtaining the overall structural deformation distribution. This article proposes a curvature identification deflection curve method suitable for monitoring the deformation distribution of simply supported steel box girder structure based on quasi distributed fiber Bragg grating strain measurement technology. Theoretical exploration of the principle of strain curvature deflection curve inversion for fiber Bragg gratings. Numerical simulations of four point bending tests on simply supported box girders show that the method based on curvature identification of deflection has high accuracy, and the relative error at the mid span is only 2.14%. The fiber optic grating strain sensor encapsulated in a stainless steel tube was arranged on the surface of a simply supported steel box girder with a span of 2 meters, and a good linear correlation was obtained between the structural deformation distribution and strain distribution. The maximum relative error between the inverted deflection and the dial gauge at the mid span was less than 3.80%, providing a reference scheme for the long-term deformation monitoring of box girders with distributed distribution.