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Shared control structure is beneficial to steering controller design of intelligence vehicles, and human-machine goal consistency is a key prerequisite for shared control. However, the goal consistency is usually given and cannot be changed, and the steering controller in low goal consistency, which directly affect the vehicle performance in case of emergency, has not been sufficiently investigated. This paper proposes a shared steering controller for path-following task based on Nash game strategy and steer-by-wire system considering different human-machine goal consistency. The driver-automation interactive path-following task is modeled by non-cooperative MPC, and authority weight of lateral displacement is used to balance the control objectives of the driver and automation. Human-machine goal consistency is determined by the driver and the automation controller steering angle. Aimed at different goal consistencies, a continuous authority weight adjustment algorithm is designed to ensure correct path following. This is especially true in low consistency in this study, when four driving modes are given to meet the different demand for control power. Simulations and hard-in-loop tests are conducted to verify the proposed control algorithm and the results show that it can perform the path-following task irrespective of human-machine goal consistency. [ABSTRACT FROM AUTHOR]