Nanoantenna enhanced fluorescence is a promising method in many emergent applications such as single molecule detection. However, the excitation wavelengths and the emission wavelengths of emitters could be well-separated depending on their Stokes-shifts, preventing optimal fluorescence enhancement by a rudimental nanoantenna. Here we propose an Ag-Si hybrid stack nanoantenna, which comprises an Ag bottom cylinder and a Si top cylinder, to match the Stokes-shift of the fluorescence emitter. The Ag cylinder is designed to resonate at the excitation wavelength of the emitter, yielding a large field enhancement to boost the excitation rate of the emitter. Meanwhile, the resonance of the low loss Si cylinder is designed to match the emission wavelength of the emitter, boosting the radiative decay rate by more than one order of magnitude and maintaining a high quantum yield. As a result, all-round enhancements in the fluorescence emission are achieved. Preliminary studies show that the hybrid stack nanoantenna can produce two times more fluorescence enhancement, and 20 times larger far field intensity comparing to those of a pure metallic nanoantenna. On top of that, around 70% of the overall radiation has been directed towards the dielectric cap side, which would be beneficial to the collection efficiency. This design fully leverages the advantages of both metal and dielectric, which could be useful in the fluorescence enhancement applications.