Nanofluids have made a breakthrough contribution toward maximizing the efficiency of heat exchangers. Consequently, graphene nanofluids have attracted significant attention, as they yield the best heat-transfer enhancement among all nanofluids; however, graphene is highly expensive, and further studies on hybrid graphene nanofluids are required to optimize costs. Research has been performed on the performance of pure graphene nanofluids, though little has been conducted on hybrid graphene nanofluids. Therefore, we investigated the hydrodynamic and convective heat-transfer performance of graphene-titanium dioxide composite (GTNC) nanofluid in a micro-heat exchanger, and compared the results with the performance of pure graphene and pure titanium dioxide nanofluids under similar conditions.Herein, we report the synthesis of GTNC using our novel green microsynthesis technique and the preparation of graphene, titanium dioxide, and GTNC nanofluids using a two-step method at three concentrations (0.02$0.08 wt%) using a surfactant. Furthermore, the stability and thermophysical properties of nanofluids were investigated, and nanofluids were studied for their effect on the performance of a counter-current laminar flow micro-heat exchanger at different flow rates (Re = 750-1460). Findings show that thermal conductivity enhancement of GTNC nanofluid and pure graphene nanofluid at the highest mass fraction (0.08%) was 25.8% and 31.6%, respectively, while the maximum enhancement of convective heat-transfer coefficient was 64.6% and 87%, respectively. These results indicate that hybrid GTNC nanofluid showed proximate thermal performance and stability level to graphene nanofluid with 50% less graphene content, which improves the economics of the process.