Veganism costs less than the consequences of the alternative. Although in general, you can expect to pay more for food, in the long-term veganism costs less.
As explained more in Why become vegan?, vegans can often avoid expensive hospital bills, surgery, and medication. By eating vegan, you can save thousands of dollars by reducing or eliminating the need for this unnecessary treatment.
Although buying unnatural and/or non-vegan foods at a supermarket generally costs less than vegan foods from a natural foods store, eating vegan foods at home has a lower cost than regular eating of non-vegan foods at a restaurant. This doesn't mean you shouldn't eat at restaurants. However, keep in mind that if the cost factor of veganism is a major concern for you, you can save money by eating at home.
Overall, veganism will more than pay for itself over a lifetime. Shopping around, growing your own garden, and buying only what you need will also save you money.