To improve flux uniformity on a planar receiver, we propose an improved design method for a parabolic dish concentrator via the optimization of the rearrangement of each mirror unit. A new non-imaging dish concentrator is also designed. In this study, a flux homogenization optimization model is established for the target area of the planar receiver and the dish concentrator is optimized by the motion accumulation ray-tracing method combined with the genetic algorithm. Moreover, the focusing flux distribution on the optimized concentrator and parabolic dish concentrator is demonstrated, and the local concentration ratio, non-uniformity factor, peak concentration ratio, and interception efficiency on the planar receiver are investigated. Finally, the potential applications of the new concentrator are discussed and the effect of the optimized dish concentrator on the flux homogenization of the planar metal coil receiver is verified. Results show that the non-imaging dish concentrator has the best effect on flux homogenization. It can significantly reduce the non-uniformity factor from 3.62--4.22 to 0.18--0.25 and the peak concentration ratio from 24737--37245 to 1722--2055. This work provides an advanced solution for the flux homogenization of planar solar receivers and an innovative idea to improve the existing parabolic dish concentrators.