With gas production moving into the deep sea, the prediction of hydrate formation and blockage prevention are of great significance in flow assurance. In this work, hydrate formation experiments at a wide range of pressures and temperatures based on the production conditions of the Lingshui gas field were conducted by a high-pressure rheometer, and the evolution of viscosity was investigated. The experimental results showed that the slurry viscosity changed in stages during the formation of the hydrate, and the aggregation of hydrate particles was the essential cause of the significant increase in viscosity. The more severe the temperature and pressure conditions, the faster the hydrate formation and the greater the tendency of increasing viscosity. In experiments, the formation of hydrates would lead to severe blockages when the pressure exceeded 10 MPa. Compared with 100 and 300 rpm, the average hydrate formation rate was the fastest at 200 rpm. In addition, the relationship between hydrate volume fraction and viscosity was analyzed, and a critical hydrate volume fraction was proposed for a sharp increase in viscosity, which had a low value at high pressures and low temperatures and tended to cause blockages. This study can provide helpful theoretical support for hydrate formation prediction and blockage prevention in natural gas production.