If you have a Shureflow 4008 "bypass" pump it has two adjustment screws hi and low pressure, that likely need adjustment. A common problem with these pumps. This pump is designed to run at a steady speed no matter the volume of water requested by the faucet the unneeded water is bypassed back to the tank, just like the fuel pump in your car operates. If it is some other brand or model likely something already mentioned above.
Lazy Days RV in Tampa has a great video on their site explaining this.
Note: the instruction manual specifically warns against using an accumulator tank with this type of pump so be sure of what you have prior to making mods.