Contrary to the monotype intercell connection in a hexagonal structure material, newly synthesized stable monolayer C60 fullerene (mC60) lattice possesses two kinds of intercell connection, and anisotropic properties are thus expected. Herein, we have investigated the anisotropy mechanical properties of the mC60 using first -principles calculations within the framework of density functional theory (DFT) and theoretical analysis. Uni-axial tensile properties of mC60 are orientation-dependent, and the ultimate tensile strength and the work-to -fracture of mC60 reach their maxima at 15 degrees and minima at 75 degrees, respectively. A theoretical expression, based on strain-governed bond failure criterion, has been developed for the strength-loading direction relationship of mC60. The theory captures well with the orientation-dependent strength from DFT calculations. We further illustrate that mC60's band gap may be largely tuned through strain engineering. Our atomistic insights and the theoretical on the structure - mechanical property relationship might be helpful in the exploring of the func-tioning and application of mC60, which may be further generalized to the mechanical analysis of other monolayer lattices.