Your statement is true but just to an extent, and false otherwise. There are cases where the pressure from the Van der Waals pressure is higher than the pressure from the Ideal Gas Law and lower in other cases. The Van der Waals equation introduces two corrections to the Ideal Gas Law, the volume correction factor & the pressure correction factor-
Pressure CF: It accounts for attractive forces between gas particles. This means that the Van der Waals pressure can be lower than the Ideal Gas pressure.
Volume CF: It accounts for the small but nonzero volume of the particles. This means that the Van der Waals pressure can be higher than the Ideal Gas pressure.
Depending on the amount and nature of your gas, the volume and the temperature, either one of these effects can dominate and thus pressure will be either higher or lower than an ideal gas (at similar conditions)!
P.S. Mark this post as a solution if this was the answer you were expecting. Have a good day!