This experimental study evaluated the thermal-hydraulic performance of a mini-channel shell-and-tube heat exchanger using graphene-water nanofluid prepared by a two-step method. Stability was verified by zeta-potential measurements and sedimentation observations; the absolute zeta-potential exceeded 30 mV at pH 7 and above, and no visible sedimentation occurred after 72 h. Six nanoparticle volume fractions (0.02%, 0.1%, 0.2%, 0.4%, 0.6%, and 0.8%) were tested. The convective heat-transfer coefficient, friction factor, thermal enhancement factor (TEF), and performance evaluation criterion (PEC) were evaluated. Graphene-water nanofluid enhanced heat transfer relative to water at all concentrations. The highest heat-transfer performance occurred at 0.6%, while the increase in friction factor remained below 20%. The best overall thermal-hydraulic performance was obtained at 0.4% and 0.6%; the maximum PEC was 1.388 at 0.6%, and the maximum TEF was approximately 1.55 at 0.4%, indicating a favorable balance between heat-transfer enhancement and hydraulic penalty. These results demonstrate that optimized graphene-water nanofluids can improve small-scale heat-exchanger performance, particularly under transitional-flow conditions, without an excessive friction penalty.