In practice, carbon capture processes in CCS (Carbon Capture and Storage) consist of two main units: the carbon dioxide (CO2) capture plant and the CO2 compression unit. This study considered a hybrid capture system that combined both the capture and the compression units. In doing so, the conventional multistage CO2 compression unit was replaced with a low-temperature carbon capture separation and pressurising step. The advantages of replacing the compression unit are two-folds: firstly, the lowtemperature separation unit can further purify the CO2 stream and secondly, it produces liquid CO2 that can be pumped to the supercritical state required for transportation and sequestration. In order to take advantage of the extra CO2 purification of the low-temperature separation unit, a vacuum swing adsorption (VSA) was used as the initial CO2 recovery stage. A hybrid process has a higher degree of freedom available and therefore a Multi-Objective Optimisation (MOO) technique in combination with heat integration was used to optimise the total shaft work and the overall CO2 recovery rate of the capture process. The MOO provided a range of optimal solutions where the total shaft work increased with the total CO2 being recovered by the hybrid process. However, a minimum optimum was determined for the total specific shaft work required at an overall recovery rate of 88.9%, which required 1.40 GJ/(t CO2 captured).