The quantum spin Hall effect (QSHE) in silicene is investigated using first-principles calculations. Silicene, a two-dimensional hexagonal structure of silicon, exhibits nontrivial topological properties due to strong spin-orbit coupling (SOC) and a low-buckled geometry. The study shows that silicene can realize QSHE with a spin-orbit band gap of 1.55 meV at low temperatures, much higher than that of graphene. Under pressure strain, the gap increases to 2.90 meV. The QSHE is confirmed by calculating the Z2 topological invariant, which is non-zero, indicating a nontrivial band topology. The low-buckled structure of silicene allows for direct hybridization between π and σ orbitals, enhancing the SOC and the gap. The Z2 invariant is calculated using a lattice method, confirming the nontrivial topology. Germanium, with a similar low-buckled structure, also exhibits a large SOC-induced band gap of 23.9 meV. The study shows that both silicene and germanium have nontrivial topological properties in their native structures, making them promising for spintronics applications. The results are supported by first-principles calculations and are consistent with experimental observations of silicene. The findings suggest that silicene and germanium with low-buckled honeycomb structures are promising materials for quantum spin Hall effect and other topological applications.The quantum spin Hall effect (QSHE) in silicene is investigated using first-principles calculations. Silicene, a two-dimensional hexagonal structure of silicon, exhibits nontrivial topological properties due to strong spin-orbit coupling (SOC) and a low-buckled geometry. The study shows that silicene can realize QSHE with a spin-orbit band gap of 1.55 meV at low temperatures, much higher than that of graphene. Under pressure strain, the gap increases to 2.90 meV. The QSHE is confirmed by calculating the Z2 topological invariant, which is non-zero, indicating a nontrivial band topology. The low-buckled structure of silicene allows for direct hybridization between π and σ orbitals, enhancing the SOC and the gap. The Z2 invariant is calculated using a lattice method, confirming the nontrivial topology. Germanium, with a similar low-buckled structure, also exhibits a large SOC-induced band gap of 23.9 meV. The study shows that both silicene and germanium have nontrivial topological properties in their native structures, making them promising for spintronics applications. The results are supported by first-principles calculations and are consistent with experimental observations of silicene. The findings suggest that silicene and germanium with low-buckled honeycomb structures are promising materials for quantum spin Hall effect and other topological applications.