In order to improve the output power of solar-pumped single-crystal fiber (SCF) lasers, we propose a novel solar concentrating system, to the best of our knowledge, consisting of a parabolic mirror, a 3D compound parabolic concentrator, and a hollow-core reflector. By ray tracing with TracePro, the influence of the fiber's diameter and the hollow reflector's shape on the solar absorption efficiency is theoretically investigated. A typical Nd:YAG SCF with a core diameter of 1 mm, length of 150 mm, and doping concentration of 1 at.% is selected for a simulation of laser operation. The output characteristics of the laser are analyzed by solving the rate equation and power transmission equation; the maximum output power and solar-to-laser conversion efficiency are 60.62 W and 4.64%, respectively. The thermal effects of the laser are simulated by Comsol software. When the input solar power is 1307.4 W, the temperature decreases sharply first and then saturates along the SCF fiber, with the maximum value of 69.18°C at the input fiber end. This concentrating system can effectively overcome the limitation of end-launching solar power into SCFs and has great potential in improving the output power of solar fiber lasers.