SNPT-U is a neutral particle transport solver based on parallel Sn transport sweep on unstructured meshes. Discontinuous Galerkin (DG) and discrete ordinate (Sn) methods are adopted for discretizing spatial and angular variables of the Boltzmann equation, respectively. The order of computation for each mesh element along single direction in the Sn transport sweep can be represented as a directed dependence graph (DDG). Sn transport sweep on unstructured meshes is performed in parallel by handling the sweeping process as a topological traversal of DDGs. However, DDGs may contain cycles in Sn sweep on 3D unstructured meshes, which leads to deadlock of sweeping. Modified DCSC algorithm is implemented for parallelly detecting cycles in the DDGs, and all the detected cycles are broken. The detection and breaking operations are kept until no cycles exist in the DDGs. SNPT-U is implemented with the JAUMIN programming framework for large-scale numerical simulation on unstructured meshes. SNPT-U is well verified with the method of manufactured solution and the neutral particle transport benchmark problems in fixed source and eigenvalue modes.