A seven-rod/seven-TEM00 mode beam Fresnel lens solar laser pumping approach is here proposed. The Fresnel lens with 4.0 m2 collection area was used as the primary solar concentrator to pump seven 2.5 mm diameter, 15 mm length Nd:YAG rods within a conical pump cavity through a secondary fused silica aspheric concentrator. Within the pump cavity, solar pump rays not completely absorbed by one of the seven rods were furtherly absorbed by other rods, ensuring hence a high absorption efficiency and avoiding the serious thermal lensing and thermal stress issues associated with classical large rod solar lasers. Seven individual plane-concave large-mode resonators were adopted to enable a good overlap between solar pump mode and TEM00 laser oscillating mode. By using both zemax® and lascad® software, the maximum total TEM00 mode solar laser power of 54.65 W was numerically calculated by optimizing the radius parameter of the Fresnel lens, the diameter of the laser rod, and the radius of curvature of the laser resonator output mirror. TEM00 mode solar laser collection efficiency of 13.66 W/m2 and solar power-to-TEM00 mode laser power conversion efficiency of 1.44% were calculated, representing substantial enhancements of 4.66 times and 4.38 times, respectively, as compared with previous experimental records of the TEM00 mode solar laser pumped through a Fresnel lens with 0.785 m2 collection area. The feasibility of TEM00 mode solar laser power delivery by hollow-core photonic crystal fibers was finally studied.