Low-frequency　response,　strong　nonlinearity　and　unknown　disturbances　are　the　main　challenges　faced　by　the　engineering　application　of　the　pump-controlled　electro-hydraulic　steering　systems　(EHSSs)　for　heavy　vehicles.　To　solve　the　above　problems,　an　active　disturbance　suppression　controller　is　proposed　based　on　a　variable　rate　reaching　law　(VRRL)　and　a　terminal　sliding　mode　observer　(TSMO)　in　the　framework　of　the　sliding　mode　control.　This　controller　is　unique　because,　the　VRRL　introduces　a　nonlinear　activation　function,　which　enables　smooth　switching　between　multiple　reaching　rates,　effectively　improving　the　response　speed　and　the　disturbance　rejection　performance　of　the　pump-controlled　EHSS.　Furthermore,　an　adaptive　incomplete　disturbance　compensation　control　strategy　is　proposed　by　incorporating　a　TSMO　to　further　improve　the　accuracy　and　robustness　of　the　steering　system,　which　employs　a　VRRL-based　TSMO　to　realize　accurate　estimation　of　the　lumped　disturbance　in　finite　time,　and　avoids　controller　overcompensation　by　selecting　a　preferred　disturbance　compensation　coefficient.　The　stability　analysis　demonstrates　that　the　proposed　controller　effectively　suppresses　the　lumped　disturbance　and　reduces　the　convergence　domain　of　the　steering　system.　A　pump-controlled　EHSS　experimental　bench　is　constructed,　and　a　series　of　experiments　are　conducted　with　various　steering　frequencies　and　load　conditions,　which　validate　the　ability　of　the　proposed　controller　to　achieve　highprecision　dynamic　steering　in　all-terrain　conditions　of　the　pump-controlled　EHSS　for　heavy　vehicles.