Haptic guidance in a shared steering assistance system has drawn significant attention in intelligent vehicle fields, owing to its mutual communication ability for vehicle control. By exerting continuous torque on the steering wheel, both the driver and support system can share lateral control of the vehicle. However, current haptic guidance steering systems demonstrate some deficiencies in assisting lane changing. This study explored a new steering interaction method, including the design and evaluation of an intention-based haptic shared steering system. Such an intention-based method can support both lane keeping and lane changing assistance, by detecting a driver lane change intention. By using a deep learning-based method to model a driver decision timing regarding lane crossing, an adaptive gain control method was proposed for realizing a steering control system. An intention consistency method was proposed to detect whether the driver and the system were acting towards the same target trajectories and to accurately capture the driver intention. A driving simulator experiment was conducted to test the system performance. Participants were required to perform six trials with assistive methods and one trial without assistance. The results demonstrated that the supporting system decreased the lane departure risk in the lane keeping tasks and could support a fast and stable lane changing maneuver.