The application of non-excavation construction technology, such as the pipe jacking method, has obvious advantages in building urban underground space engineering projects, which can effectively reduce the occupation of ground surfaces and the migration of obstacles above or below the ground. However, pipe jacking machines with a rectangular cross-section can easily encounter great difficulty due to the significantly increased jacking resistance while it is jacked in hard rock strata, which are often influenced by large blind spots on the working face of pipe jacking machines with a rectangular cross-section. The aforementioned blind spots belong to areas that cannot be cut by the cutter heads due to the circular cutterhead and rectangular outer frame of pipe jacking machines with a rectangular cross-section. Therefore, the effective pretreatment of the aforementioned blind spots should be implemented prior to operating pipe jacking machines with a rectangular cross-section in hard rock strata. This paper presents a case study of employing horizontal-directional drilling as a multi-pilot heading pretreatment for breaking large blind spots on the working face of pipe jacking machines with a rectangular cross-section, which was implemented prior to operating a pipe jacking machine with a rectangular cross-section in shallow buried rock strata. In particular, this multi-pilot heading pretreatment is expected to be used to safely construct a rectangular comprehensive pipe gallery using pipe jacking machines with a rectangular cross-section in shallow buried rock strata and when passing underneath existing light rail lines, which can effectively save the precious land resources required for sustainable development. The study was implemented by employing a numerical simulation, focusing on the safety of the adjacent existing light rail line and the stability of the surrounding rocks, which are influenced by the variation in the distribution positions and sizes of the drilling holes used when implementing the horizontal-directional drilling. The results demonstrate that the horizontal-directional drilling applied for the multi-pilot heading pretreatment could effectively break the blind spots on the working face of the pipe jacking machine with a rectangular cross-section, in which the safety of the adjacent existing infrastructure was significantly influenced by the distribution positions and sizes of the drilling holes used when implementing the horizontal-directional drilling. This study can provide a reference for carrying out pipe jacking construction using pipe jacking machines with a rectangular cross-section, in which horizontal-directional drilling is employed as the multi-pilot heading pretreatment for breaking the large blind spots on the working face. Moreover, the distribution positions and sizes of the drilling holes used when implementing the horizontal-directional drilling could be appropriately optimized by utilizing the method of numerical analysis. Meanwhile, the study is also expected to eliminate the hazards of safely running the aforementioned adjacent existing light rail line during implementing the multi-pilot heading pretreatment of horizontal-directional drilling.