In high-frequency (HF) radar systems, transient interference is a common phenomenon that dramatically degrades the performance of target detection and remote sensing. Up until now, various suppression algorithms of transient interference have been proposed. They mainly concentrate on the skywave over-the-horizon radar on the basis of the assumption that the interference is sparse in a coherent processing interval (CPI). However, HF surface wave radar (HFSWR) often faces more complex transient interference due to various extreme types of weather, such as thunderstorm and typhoon, etc. The above algorithms usually suffer dramatic performance loss when transient interference contaminates the enormously continuous parts of a CPI. Especially for the compact HFSWR, which suffers from severe beam broadening and fewer array degrees of freedom. In order to solve the above problem, this study developed a two-dimensional interference suppression algorithm based on space-time cascaded processing. First, according to the spatial correlation of the compact array, the statistical samples of the main-lobe transient interference are estimated using a rotating spatial beam method. Next, an adaptive selection strategy is developed to obtain the optimal secondary samples based on information geometry distance. Finally, based on a quadratic constraint approximation, a precise estimation method of the optimal weight is developed when the interference covariance matrix is singular. The experimental results of simulation and measured data demonstrate that the proposed approach provides far superior suppression performance.