Multi-axle heavy vehicles employ a variable-length tie rod steering system to achieve precise multi-mode steering. However, the single-axle steering system need integrate two sets of electro-hydraulic control systems (EHCSs), resulting in the energy consumption significant increase. This paper proposes a novel energy-efficient pump-valve primary-auxiliary electro-hydraulic steering system (PVPA EHSS) which compose of a pump-controlled dual-steering cylinders primary system and a valve-controlled variable-length tie rod cylinder auxiliary system. The proposed system utilizes a single pump to drive both the primary and auxiliary EHCSs simultaneously, enabling high-precision and high-efficiency steering with multi steering modes. Additionally, to suppress the flow disturbance of the auxiliary system branch flow on the single-pump-controlled steering primary system, the interaction between the flow of the auxiliary system and the flow of the primary system in each steering phase is studied. A pump flow feedforward-angle feedback composite control strategy incorporating branch flow prediction is proposed to mitigate the disturbance and ensure the accurate steering of left and right tires. The experimental results demonstrate that compared to the traditional variable-length tie rod steering system, the proposed system reduces energy consumption by 58.66 %, and achieves precise adaptation of the left and right tire angles in multi steering modes.