The company says it is consolidating its services and call centers. Verizon says it will help some of the employees find other jobs within the company and it will give help if employees who are willing to relocate.
Those who don't get other jobs in the company will get severance packages.
The southwest Houston call center is expected to close in the next several months. The company's regional headquarters will remain in Houston.
Verizon is closing other centers in Washington state and Michigan, so the changes will affect about 3,000 in total.
In a statement, the company said it was "a very difficult but necessary business decision."