A hexagon-shaped floating unit (HS-FU) was proposed, and the optimization was performed with respect to the geometric dimension based on the response surface method (RSM). A multi-objective optimization model considering the total weight and heave response was established to achieve a satisfactory balance between economy and safety. Subject to the constraints of the roll response, stability height, freeboard, and collision issue, five independent design variables were optimized to achieve the minimum total weight and heave response. To reduce the computational burden and improve the optimization efficiency, surrogate models of output variables were constructed based on the RSM. The results show that, opposite to the heave response, the total weight of the floating unit is positively proportional to the side lengths of the water tank and living area; the stability performance can be improved by increasing the water tank height and the living area side length. The combination of weighting factors with a value of 0.4 for total weight and 0.6 for heave response was selected as one of the optimal designs for the floating unit. Compared with the initial design, the optimal design shows better performance, with the heave response decreasing by 22.51% and the stability increasing by 28.30%.