For the requirement of fast-response temperature of expendable ocean sensor, a new design scheme of optic fiber sensor was presented. Metal materials of different thermal expansion coefficients and the same tube structure with inner diameter d = 0.55 mm, length L = 9 mm were used for packaging FBG along the axis of a metal tube. And the temperature characteristics of the encapsulated Fiber Bragg grating (FBG) were experimentally studied. The theoretical calculation, simulation and the tests of the fast response properties were also described and analyzed in detail. The experimental results show that, the response time of the single-ended FBG packaged by a stainless tube is 47.1 ms, and the response time of the double-ended FBG packaged by a copper tube is 48.6 ms, which has increased by an order of magnitude than that of an ordinary optical fiber temperature sensor.