A vector based freeform approach is proposed for the geometrical reverse design of reflecting solar concentrators. The effect of solar cone angle of incident vectors is taken into consideration in the method based on three-dimensional freeform optics. The method developed is a closed-loop program and did not need any other commercial software. According to the transmission pattern of solar concentrators, the source-target mapping should be initially established prior to constructing an initial geometry formed by discrete points using the Geometric Construction Method. The freeform surface is generated by connecting several triangular flat elements defined by these points and then the Monte-Carlo ray tracing was conducted. The freeform surface can then be further optimized through feedback modifications. Finally, the optimal shape is obtained when the design examples are the off-axis freeform reflectors with target circular/rectangular receivers for the use of Concentrated Photovoltaic. This method provides a practical approach for improving the optical performance of solar concentrators. (C) 2017 Elsevier Ltd. All rights reserved.