Carbon-based perovskite solar cells (C-PSCs) are emerging as low-cost stable photovoltaics. However, their power conversion efficiency (PCE) still lags behind that of devices based on Au or Ag as the current collector. Here, we introduced an innovative modular PSC design using a carbon back electrode, whose sheet resistance and thickness were greatly reduced by covering it with another carbon-coated FTO glass that was applied under pressure. We showed that these two individual elements could be assembled and separated repeatedly. Moreover, among the various commercial carbon sources (carbon black, graphite sheet, and graphene), graphene exhibited the best overall performance, showing the crucial importance of graphene as a charge collector. Power conversion efficiency (PCE) of 18.65% was achieved for graphene-based PSCs (G-PSCs), which was among the highest efficiency reported so far for C-PSCs. Moreover, the optimized devices without encapsulation retained 90% of their initial PCE after aging at an elevated temperature of 85 degrees C for 1000 h. Remarkably, G-PSCs showed significant structural flexibility; there was negligible degradation in PCE after repeated disassembling and assembling for more than 500 cycles. Our system provides a promising prospect for the facile repair and maintenance of PSCs via modular interconnections; related strategies may be extended to other devices.