To mitigate the risk of manufacturing defects and improve the efficiency of the autoclave-processed thick composite component curing process, parameter sensitivity analysis and optimization of the curing profile were conducted using a finite element model, Sobol sensitivity analysis, and the multi-objective optimization method. The FE model based on the heat transfer and cure kinetics modules was developed by the user subroutine in ABAQUS and validated by experimental data. The effects of thickness, stacking sequence, and mold material on the maximum temperature (Tmax), temperature gradient (ΔT), and degree of curing (DoC) were discussed. Next, parameter sensitivity was tested to identify critical curing process parameters that have significant effects on Tmax, DoC, and curing time cycle (tcycle). A multi-objective optimization strategy was developed by combining the optimal Latin hypercube sampling, radial basis function (RBF), and non-dominated sorting genetic algorithm-II (NSGA-II) methods. The results showed that the established FE model could predict the temperature profile and DoC profile accurately. Tmax always occurred in the mid-point regardless of laminate thickness; the Tmax and ΔT increased non-linearly with the increasing laminate thickness; but the DoC was affected slightly by the laminate thickness. The stacking sequence has little influence on the Tmax, ΔT, and DoC of laminate. The mold material mainly affected the uniformity of the temperature field. The ΔT of aluminum mold was the highest, followed by copper mold and invar steel mold. Tmax and tcycle were mainly affected by the dwell temperature T2, and DoC was mainly affected by dwell time dt1 and dwell temperature T1. The multi-objective optimized curing profile could reduce the Tmax and tcycle by 2.2% and 16.1%, respectively, and maintain the maximum DoC at 0.91. This work provides guidance on the practical design of cure profiles for thick composite parts.