The forward kinematics of the Stewart–Gough platform is vital for high-precision positioning and sensing in six degrees of freedom. In this paper, the solving of forward kinematics is converted to searching for the best posture corresponding to the input outrigger length vectors by inverse kinematic calculation. The simulated annealing (SA) process is embedded into particle swarm optimization (PSO) to improve the convergence speed and overcome the local convergence. The proposed SA–PSO algorithm not only accelerates the convergence speed but also improves the reliability and success rate. After the optimization of algorithm parameters, the success rate of the SA–PSO for random outrigger length vector input is steadily above 99.9% while the results of PSO is between 93% and 100%. In the workspace simulation, the average iteration number of the proposed algorithm is reduced from 146.6 to 122.7, meanwhile, the success rate of SA–PSO is 99.992%, much higher than the 93.805% of PSO. Compared with the traditional Newton–Raphson method, the SA–PSO method has a higher success rate and is less time consuming. Finally, a physical experiment is conducted on a six-degree-of-freedom platform, revealing that the given algorithm is reliable and accurate.