We present a scheme to construct grand unified models based on the superconformal algebra and the inclusion of matter fields in the adjoint representation of supersymmetry. As an illustration, we implemented the Georgi-Glashow SU(5) model. The model predicts the existence of a dark (1,24, 0) + (5,5*, −y′) + (5*,5, y′) sector and an anomalous U(1)Z.