As the electrification of vehicles continues to become more widespread, the electric brake system is also continuously improving. This has led to higher demands on the capabilities and performance of active braking and regenerative braking in the field of vehicle dynamics control. Therefore, this paper proposes a novel pressure demand control approach for the electro-hydraulic brake-by-wire system, aimed at accurately and swiftly tracking the target pressure. Firstly, we establish a simplified model of the system and use a second-order function to approximate the pressure-position relationship. The sliding mode control is employed to convert the desired pressure into the required piston position. Then, the kinematic relationship is used to convert it into the motor rotation angle. Moreover, we apply a proportional-integral controller to adjust the motor rotation angle, and further fine-tune the controller parameters using a particle swarm optimization algorithm. Finally, a joint simulation platform are built, and a brake test bench is established for three pressure signal tests. The experimental results demonstrate that the pressure demand control method achieves precise tracking of the target pressure, with a maximum error not exceeding 2%. Compared to other methods, this approach exhibits superior control accuracy and response characteristics.