An algorithm is introduced to minimise the beam angle of compound parabolic concentrators (CPCs) with LED sources under the condition of a fixed exit aperture, as a big beam angle will cause large off-axis aberration and low efficiency for a projection system. According to the edge-ray principle and coordinates transform, the formula for the algorithm is derived with LED sources considered as extended sources. In this paper, an example is given to prove the algorithm. Not only the minimum beam angle but also the specific parameters of CPCs can be obtained by this algorithm.