A deduction of a solution of the Einstein's equations, employing the Mitskievich's field theoretic description of perfect fluids, is presented. This solution describes a dust-space-time with a spherical-like symmetry and a NUT-like rotation. This solution is of Petrov type D, and has an isometry group G4. It also admits closed timelike geodesics. It has Minkowski space-time as a limit, when both dust and rotation disappear.