Optimization method, as a promising way to improve inlet aerodynamic performance, has received increasing attention. The present research is undertaken to design a two-dimensional axisymmetric hypersonic inlet using parametric optimization. The inlet configuration is parameterized and optimized in consideration of total pressure recovery and starting performance. A Pareto front is obtained by solving the multi-objective optimization problem. Then, the flow structures of the optimized inlets are analyzed and the starting performances are evaluated. Results show that the total pressure loss mainly occurs in the internal contraction section, especially near the inlet entrance, and therefore the total pressure recovery coefficient can be greatly improved by decreasing external compression. As a result, the guidance for designing high-performance inlets is concluded. Besides, it is found that as the internal contraction ratio increases, the inlet starting ability becomes worse, which attributes to the larger separation bubble at the inlet entrance. Finally, the total pressure recovery coefficient and the starting Mach number of the optimized inlets are obtained, which can be a reference for engineering design.