Single-layer FeSe film grown on SrTiO3(001) surface (STO surface) by molecular beam epitaxy has aroused a great research boom ever since the discovery of its huge superconductive energy gap which indicates a possible critical temperature (Tc) higher than the liquid nitrogen temperature. The interface enhanced superconductivity with a Tc above 100 K is revealed in an in situ electrical transport measurement by using a four-point probe installed in a scanning tunneling microscope (STM). Consequent research interest in multi-layer FeSe films grown on STO surface is also increasing. The quality of thick FeSe film, however, has not been well studied yet in previous studies, although it is related to the sample properties including superconductivity. Here, reflection high-energy electron diffraction (RHEED) is used to monitor the growths of multi-layer FeSe thin films on STO surface under different growth conditions. Combing the RHEED results with STM observations taken at various FeSe coverages, we find that the intensity evolution of the RHEED pattern in the early growth stage can be well explained by the step density model but not by the widely known facet model. The intensity evolution of the FeSe(02) diffraction streak exhibits a single-peak oscillation in the growing of the first layer of FeSe. As the oscillation does not depend on the grazing angle of the high-energy electron beam, the FeSe(02) diffraction streak is very suitable for calibrating the FeSe growth rate. In contrast, the intensity of the specular spot exhibits different evolution pattern when the grazing angle of electron beam is changed. It is found in STM observations that only at an appropriate substrate temperature and a growth rate can the high-quality multi-layer FeSe films be grown on STO substrates. If the growth temperature is too high, the FeSe molecules nucleate into islands so that FeSe films with various thickness values eventually come into being on the STO surface. If the growth temperature is too low, a different phase of FeSe film is formed. The optimal growth temperature is in a range from 400 ℃ to 430 ℃, within which a two-layer FeSe film grown at a low rate (0.15 layer/min) coveres the whole STO surface with a negligible number of small FeSe islands. In contrast, a larger growth rate is necessary for growing thicker FeSe film. This is because FeSe islands tend to come into form at steps when the growth rate is too low, which is more distinct in a thicker FeSe film. An STM image of 80-layer FeSe film grown under an optimal condition, i.e., the substrate temperature of 420 ℃ and the growth rate of 2.3 layer/min, shows that it is in a perfect layer-by-layer growth mode. These experimental results are useful for growing high-quality multi-layer FeSe films on STO substrates, which could be critical for studying their physical properties and relevant physical phenomena.