According to the mass law, it is impossible to increase sound transmission loss (STL) of conventional structures at low frequencies without increasing their weight. Metastructures are capable to break the limits of the mass law at low frequencies. However, many existing sound insulation metastructures need to be constructed using a host structure with low-stiffness properties, such as a thin plate and a thin membrane. As a result, the metastructures normally have large exposed areas with low-stiffness characteristics and are unable to bear heavy loads, which limits their practical applications. In this work, we propose a high-stiffness plate-type metastructure (HSPM) with both low-frequency sound insulation performance and high stiffness properties. The STL performance of the HSPM is demonstrated analytically, numerically and experimentally, indicating that the HSPM can deeply break the mass law at low frequencies. Owing to the simple construction, high stiffness properties, and high sound insulation performance at low frequencies, the proposed HSPM has promising applications in practical noise control engineering.