Nanoclusters like fullerenes as the unit to build intriguing two-dimensional (2D) topological structures is of great challenge. Here we propose three bridged fullerene monolayers and comprehensively investigate the novel fullerene monolayer (α-C60-2D) as synthesized experimentally [Hou et al. Nature 2022, 606, 507-510] by state-of-the-art first-principles calculations. Our results show that α-C60-2D has a direct band gap of 1.55 eV close to the experimental value, an optical linear dichroism with strong absorption in the long-wave ultraviolet region, a small anisotropic Young's modulus, a large hole mobility, and an ultrahigh Seebeck coefficient at middle-low temperatures. It is unveiled that the anisotropic optical, mechanical, electrical, and thermoelectric properties of α-C60-2D originate from the asymmetric bridging arrangements between C60 clusters. Our study promises potential applications of monolayer fullerene networks in lots of fields.