The object of the present paper is to study spacetimes admitting quasi-conformal curvature tensor. At first we prove that a quasiconformally flat spacetime is Einstein and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying Einstein’s field equation with cosmological constant is covariant constant. Next, we prove that if the perfect fluid spacetime with vanishing quasi-conformal curvature tensor obeys Einstein’s field equation without cosmological constant, then the spacetime has constant energy density and isotropic pressure and the perfect fluid always behave as a cosmological constant and also such a spacetime is infinitesimally spatially isotropic relative to the unit timelike vector field U. Moreover, it is shown that in a purely electromagnetic distribution the spacetime with vanishing quasi-conformal curvature tensor is filled with radiation and extremely hot gases. We also study dust-like fluid spacetime with vanishing quasi-conformal curvature tensor. © 2016 Iranian Mathematical Society.