In order to obtain the copper-titanium bimetallic composite tube with excellent forming quality and small relative bending radius (R/D2≤2, D2 is the outer diameter of the covered tube), a finite element model for bending-springback process of copper-titanium bimetallic composite tube is established based on the ABAQUS/Explicit finite element platform in this paper, and the wrinkling limit of the copper-titanium bimetallic composite tube with small radius bending is simulated and analyzed by finite element method. That is, with a rigid mandrel and different numbers of mandrel cores filling, the minimum relative bending radius (R/D2)min to prevent wrinkling is obtained. The results show that, the cross-section deformation rates φ in both the base tube and covered tube filling zones are significantly smaller than those in the non-filling zone. The φ in the filling zone slightly increased with the decrease of R/D2, while the φ in the non-filling zone significantly increased with the decrease of R/D2. This indicates that the tendency for wrinkling in the cross-section of the non-filling zone is significantly higher than that in the filling zone. R/D2=1.76 is the turning point for wrinkling occurrence. When R/D2=1.76, one core filling does not meet the forming quality requirements. When two and three cores are filled, it meets the requirements of forming quality, and the filling with two cores is better than three cores. When R/D2=1.32, wrinkles will appear under the three filling conditions, which does not meet the forming quality requirements. To determine the minimum relative bending radius, further analysis was carried out on the wrinkling of the composite pipe with two mandrel cores filling and R/D2=1.71, R/D2=1.74. It is found that number of wrinkles N=1 and φmax exceeded 5%, which does not meet the forming quality requirement. Therefore, the forming limit of the copper-titanium bimetallic composite tube is two mandrel cores filled and (R/D2)min=1.76.