The Cs2AgBiBr6 was among the earliest double perovskite investigated to address the toxicity and instability challenges of perovskites solar cells (PSCs). Unfortunately, the unstable hole transport layer (HTL), limited carrier diffusion length, abundant interface defects, and inferior hole extraction efficiency result in unsatisfactory device performance. Here, we propose a novel Cs2AgBiBr6 carbon-based double perovskite solar cell (C-DPSC) without an HTL to enhance device performance. The Cs2AgBiBr6 C-DPSC is achieved by optimizing absorber layer thickness, gradient structure (doping gradient, gradient defects, and gradient energy bands), average doping density, and interface defect density through Solar Cell and Capacitance Simulator (SCAPS). The gradient structure in Cs2AgBiBr6 C-DPSC exhibit the excellent average defect tolerance density of 1016 cm-3 and enhanced built-in electric field, facilitating the effective separation of photogenerated electron-hole pairs. Moreover, the formed gradient energy bands have a negligible impact on the overall device performance. Compared to the conventional Cs2AgBiBr6 PSC with an HTL, which exhibited an open-circuit voltage of 1.09 V, a short-circuit current of 3.80 mA/cm2, a fill factor of 40.23 %, and a power conversion efficiency of 1.67 %, the corresponding electrical parameters of Cs2AgBiBr6 C-DPSC with an optimized gradient structure was elevated to 1.69 V, 12.11 mA/cm2, 88.79 %, and 18.21 %, respectively. This work provides recommendations and guidance for manufacturing economical and efficient free-Pb PSCs.