In this study, the efficiency of a large aperture 2-stage parabolic trough concentrator (PTC) is improved using an innovative design method for the secondary reflector (SR). The design method is based on an adaptive approach in which the SR is step-wise optimized to maximally reflect back to the absorber tube (AT) the part of solar radiation reflected by the primary reflector (PR) but not captured by the AT. The adaptive design method results in a SR design which consists of several parabolas with different focal lengths, each having a focus which lies in the focus of the PR. This ensures that the originally unabsorbed solar radiation will now hit the surface of AT. The optical efficiency of the PTC could be increased by 5.2% and thermal efficiency by 4.9%, respectively, compared to a case without optimized SR. In addition, the uniformity of the solar radiation flux on the AT's outer wall could be doubled, its temperature was more even. The new adaptive design approach of the SR could help to better optimize PTC systems.