Various plants have the ability to follow the sun with their flowers or leaves via a mechanism known as heliotropism, which is powered by pressure gradients between neighboring motor cells. Adapting this bio-inspired mechanism, in this paper we present a novel origami-inspired pneumatic solar tracking system for a picosatellite named NPU-PhoneSat that is capable of solar tracking without altering the attitude of the NPU-PhoneSat. We give an overview of the system design and address the theoretical problem of modeling the origami-inspired pneumatic solar tracking system. The theoretical results are compared with the experimental data, demonstrating the validity of the proposed analytical model. Such understanding of soft solar trackers will allow their performance to be predicted, thus enabling their wide utilization in enhancing energy supply.