Natural gas hydrates (NGHs) are considered as a powerful potential energy resource. In this work, an experimental system containing a digital electrical bridge for resistance measurement was developed to gain an improved understanding of the formation/dissociation characteristics of NGHs in consolidated sediments. Using the apparatus, a dynamic methane hydrate formation method for sandstone cores was developed that can maintain a constant gas flow in the core during the methane hydrate formation process. As opposed to the traditional method that maintains a constant pressure in the core, higher resistance, permeability, and hydrate saturation for the core were obtained following methane hydrate formation equilibrium by using the proposed method. In order to investigate the methane hydrate formation characteristics in sandstone cores, the influences of core permeability, temperature, initial water saturation, and salinity on the resistance and hydrate saturation of two cores were analyzed in detail. The experimental results demonstrate that a relative lower temperature and higher initial water saturation in the core correspond to a higher hydrate saturation and water-to-hydrate conversation ratio. In the process of methane production from continent hydrate, the water output from the core with methane extraction was experimentally measured for the first time. It was found that, owing to the existence of free gas in the core holder, both the core resistance and methane production rate were not changed linearly with time. The methane production amount increased with an increase in initial water saturation, decrease in production pressure, or increase in pore volume in the core. It was demonstrated that water output is not a serious problem in the development of continental natural gas hydrate.