A collapsible desk assembly includes a desk board, an elbow joint, a positioning board, and a connecting portion. The elbow joint has a groove defined therein and is mounted to the desk board. The positioning board has a pin disposed thereon and the positioning board is connected to the elbow joint. The pin is inserted into the groove. A pivoting shaft is extending from the positioning board. The connecting portion has a receiving hole defined therein for receiving the pivoting shaft. A bolt is inserted into the receiving hole and passing through the pivoting shaft, and is threaded to the elbow joint. When the desk board is descended, the positioning board is rotated downwardly and blocking the elbow joint from pivotally bending relative to the connecting portion, such that the desk board is stably suspended beside the connecting portion.