A wheeled-leg pipeline robot suitable for operation in small pipes is proposed to address the challenges of detecting the condition of pipelines, such as solution corrosion and crack defects, which cannot be conducted externally due to the pre-buried pipe system embedded in other structures. Inspired by existing pipeline robots, the proposed robot employs a mechanical structure with six wheeled legs arranged in an alternating pattern. To analyze the motion state of the pipeline robot turning in curved pipes, kinematic analysis based on geometry is conducted to figure out the kinematic characteristics of the robot navigating in curved pipes. The relationship between the motion trajectories of each contact wheel and the posture angle of the robot in the pipeline is the focal point. Additionally, a turning method preventing wheel slippage is proposed specifically for this type of robot. Finally, an experiment with the pipeline robot navigating in the curved pipeline is implemented and demonstrates successful passing through curved pipes with an inner diameter of 120 mm as well as a turning radius of 240 mm, with the effectiveness of the kinematic analysis validated.