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This article aims at solving the straight-line tracking control problem of agricultural tractors in the presence of negative influences induced by unknown disturbances. Firstly, the path tracking dynamics model with unknown disturbance is established, and then it is further converted into a third-order sliding mode (TOSM) dynamics that facilitates control design. On this basis, a straight-line tracking control strategy for agricultural tractors is proposed by using TOSM. It is demonstrated by strict Lyapunov analysis that the lateral error and heading deviation are stabilized to the origin in a finite time. Finally, the comparative simulation results show that the proposed path-tracking algorithm can achieve the control objective of straight-line tracking of agricultural tractors. [Display omitted] • The third-order sliding mode controller is proposed to handle the problem of agricultural tractor navigation. • The proposed control scheme can ensure that the tracking errors converge to zero in a finite time. • The closed-loop sliding mode dynamics can be driven to the origin in finite time. [ABSTRACT FROM AUTHOR]