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In recent years, autonomous driving technology has been developing rapidly, but there is still a certain gap from commercial production, in which the safety issue is one of the important factors. In the working of most companies and colleges, the Traffic Jam Pilot (TJP), serving as a prototypical Level 3 autonomous driving function, has predominantly focused on functional implementation and enhancement, prioritizing functional completeness and user comfort. However, the aspect of functional safety in the system has received comparatively less attention. To guarantee the safety of the driver’s life and property, it is essential to consider the functional safety aspect regarding automobile operation after system function failure. In this paper, according to the functional safety development process and related regulations in ISO 26262, the functions and operation environment of the TJP system are defined in detail, and the longitudinal function is taken as an example to be developed following the functional safety process and verified by simulation. Simulation verification results show that the control algorithm is safe and reliable, and can ensure the safety and stability of the vehicle during operation. The research in this paper further explores the combination of functional safety and high-level automated driving function, providing some ideas for their practical application in industry.