Recently the charge density wave (CDW) in vanadium dichalcogenides have attracted increasing research interest, but a real-space investigation on the symmetry breaking of the CDW state in monolayer is still lacking. We have investigated the CDW of monolayer by low energy electron diffraction (LEED) and scanning tunneling microscope (STM). While the LEED experiments revealed a CDW transition near 192 K, our low-temperature STM experiments resolved the lattice distortions and charge-density modulation in real space, and further unveiled a one-dimensional structural modulation that breaks the threefold rotational and mirror symmetries in the CDW state. In accordance with the CDW state at low temperature, a CDW gap of 12 meV was detected by scanning tunneling spectroscopy at 4.9 K. The observed symmetry breaking implies that besides the conventional Fermi surface nesting or the -dependent electron-phonon coupling, some other mechanism may also contribute to breaking the threefold rotational symmetry in the CDW state of monolayer.