Recovering CAD models from point clouds, especially the sketch-extrusion process, can be seen as the process of rebuilding the topology and extrusion primitives. Previous methods utilize implicit fields for sketch representation, leading to shape reconstruction of curved edges. In this paper, we proposed a CAD reconstruction network that produces editable CAD models from input point clouds (Point2Primitive) by directly predicting every element of the extrusion primitives. Point2Primitive can directly detect and predict sketch curves (type and parameter) from point clouds based on an improved transformer. The sketch curve parameters are formulated as position queries and optimized in an autoregressive way, leading to high parameter accuracy. The topology is rebuilt by extrusion segmentation, and each extrusion parameter (sketch and extrusion operation) is recovered by combining the predicted curves and the computed extrusion operation. Extensive experiments demonstrate that our method is superior in primitive prediction accuracy and CAD reconstruction. The reconstructed shapes are of high geometrical fidelity.