In nano-photonics, the enhancement of the intensity of directional luminescence in fluorescent substances is a key issue for many applications. In order to optimize the fluorescence enhancement capability of dielectric nano-antennas, a dielectric hybrid nano-antenna composed of a silicon nanosphere dimer and a TiO2 microsphere is proposed. Quantum yield enhancement, fluorescence collection efficiency enhancement and fluorescence excitation rate enhancement are all studied using the finite difference time domain method to illustrate the fluorescence enhancement effect of the dielectric sphere hybrid nano-antenna. The results show that the hybrid nano-antenna can not only solve the problem with low quantum yield using the single TiO2 microsphere, but can also compensate for low fluorescence collection efficiency using only the silicon nanosphere dimer. Due to the advantages possessed by both silicon nanosphere dimers and TiO2 microspheres in fluorescence enhancement, the quantum yield and fluorescence collection efficiency of this hybrid nano-antenna are enhanced by about 4 and 2 times, respectively. Moreover, due to the further enhancement effect on the fluorescence excitation process with the silicon nanosphere dimer and the TiO2 microsphere, a higher fluorescence directional enhancement factor can be achieved. When the emission wavelength is at a quantum dot central wavelength of 523 nm, the fluorescence directional enhancement can be up to 3 064 times than that of original fluorescence.