1999 Hyundai Accent engine starving

Hi.I am working on my mothers vehicle and it will start and idle fine when you acelerate it will rev up then cut off but if you let off the gas pedal it will go back to idle and not miss or nothing. If i wait for a couple of seconds it will be able to rev up and then starve again.It seems it doesent have enough gas but we checked the gas pressure and it has plenty of pressure.what else could it be?please help me fix my mothers vehicle asap.thank you and god bless.