Organic-inorganic hybrid perovskites (PSKs) function as efficient anodes for Li-ion batteries (LIBs) due to their facile alloying-dealloying reactions between Li and Pb. A large alkyl chain containing an organic cation, specifically, 3-bromopropylamine hydrobromide (BPA), is used to synthesize a 2D-3D hybrid PSK (CsMABPAPbIBr). The bulkiness of BPA inhibits its incorporation in the 3D octahedral cages, creating a pseudoquantum well wherein the low band gap inorganic PbX6 4- (X: Br/I) octahedra serve as the potential wells, and the high band gap organic layers serve as potential barriers. This mixed-dimensional structure affords a greater number of accessible sites for Li+ ions, superior electrical conductivity and chemical stability relative to the control 3D PSK (CsMAPbIBr), thereby improving capacity, rate capability, and operational lifespan. Li-ion cells with the 2D-3D hybrid PSK-carbon nanotubes (CNTs) composite exhibited an initial discharge capacity of 221 mAh g-1, 84% capacity retention after 100 cycles and an energy density of 508 Wh kg-1, significantly enhanced compared to the 3D PSK-CNTs. The charge storage mechanism is largely dominated by pseudocapacitive-surface-controlled redox reactions, and the improved resistance to capacity fade demonstrated by the 2D-3D PSK is attributed to the ability of the organic cations (BPA) to serve as a strain-absorbing overlayer. These results highlight the potential of 2D-3D PSKs for developing energy-dense long-lived LIBs for practical applications.