We present a detailed theoretical and experimental study on the sensitivity enhancement for multimode fiber (MMF) speckle sensor. Using mode coupling theory, we derive an expression showing that the sensitivity of the MMF speckle sensor depends on the intensity profile of the MMF modes. Particularly, we use our theory to study the influence of the spatial filtering window on the sensitivity, and the experimental results have found a good agreement with the theory. Our results suggest that the sensitivity of an MMF speckle sensor can be greatly enhanced by adjusting the size and location of the spatial filtering window. An 80-fold improvement on sensitivity was achieved in our experiment, as compared with the conventional MMF speckle sensor with the filtering window placed at the center of the speckle field.