The recently discovered heavy-fermion superconductor, UTe₂, is an excellent candidate for spin-triplet superconductors where electrons form spin-triplet Cooper pairs with spin S = 1 and odd parity. Unconventional superconductivity often hosts the unconventional vortices. Yet, the vortex core and lattice in UTe₂ have not been directly visualized and characterized. In this talk, I will present our recent low-temperature STM results on the vortex core and lattice on the (0−11) surface termination of UTe₂. We observe the robust zero-energy vortex core state which extends to ~30 nm along the crystallographic a axis. I will show the unique symmetry breaking feature in the superconducting vortices of UTe₂. In addition, I will also discuss our recent STM data on the other cleavage surfaces of UTe₂.