A power steering assembly for a large vehicle including a primary booster, an auxiliary booster, a primary hydraulic oil pipe adapted to connect the primary booster to the hydraulic pump, an auxiliary hydraulic oil pipe branched off from the primary hydraulic oil pipe and adapted to connect the auxiliary booster to the hydraulic pump, a control valve provided to the primary hydraulic oil pipe at an upper stream side from the place where the auxiliary hydraulic oil pipe is branched off, and a load sensing valve provided to the auxiliary hydraulic oil pipe. When the load of the primary booster is small, the oil pressure of the primary booster is low, the load sensing valve is closed, and only the primary booster is driven, whereas when the load of the primary booster becomes large, the oil pressure of the primary booster is high, the load sensing valve opened, and the auxiliary booster is driven in association with the primary booster to supplement the steering power of the primary booster.