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A superconducting quadrupole magnet based on the Canted-Cosine-Theta (CCT) type coil with a gradient field of 40 T/m and a bore diameter of 60 mm has been designed for the preresearch of two projects of high intensity accelerator facility (HIAF) and accelerator driven subcritical system (ADS). The magnet is comprised of two-layer coils embedded in the formers and the end plates for locating. The coil formers made of aluminum alloy are machined with grooves according to the drive equations of CCT for placing the wires. The existence of ribs between two adjacent wires can avoid accumulation of the electromagnetic force. It is important to take the mechanical design for the complex structure to avoid tensile stresses on the conductor and confine the stresses within a reasonable value. The stress analysis for the quadrupole magnet has been carried out considering the thermal shrinking due to cool down as well as the electromagnetic force on the coil. This paper reports the detailed stress analysis for the CCT quadrupole magnet structure, discusses the calculating results, and gives a reasonable mechanical design.