A novel parabolic dish solar concentrator based on the improved 3-RPS parallel manipulator to drive the reflective mirror facet is proposed and designed, which can not only automatically adjust the position and orientation of the reflective mirror facet but also have the advantages of independent drive, high stiffness and no cumulative error. Then, using the coordinate transformation matrixes of the novel parabolic dish solar tracking platform, the kinematics models of the 3-RPS parallel manipulators associated with the solar altitude and azimuth angles are established. The altitude and azimuth angles of the solar movement at the installation location are calculated according to the calculation formula of solar position. To solve the problem of too many telescopic rods of the 3-RPS parallel manipulator, a genetic algorithm is used to optimize the height of the concentrator’s center of mass. Then the ideal trajectory and attitude of each telescopic rod of the 3-RPS parallel manipulators at different times of the day can be obtained with the inverse kinematics. The particle swarm optimization (PSO)-proportional-integral-derivative (PID) controller, which uses PSO algorithm to tune PID parameters, is proposed for solar trajectory tracking of the novel parabolic dish solar concentrator. The visual simulation model of the parabolic dish system is established in Simscape Multibody, and the trajectory tracking control experiment is carried out. The experimental results show that the trajectory tracking error of the novel dish solar tracking platform can be within 2.6 mm by using the PSO-PID controller.