Lyle Bensley's mugshot, courtesy of the Galveston Police Department.
Bensley groaned and hissed at the woman while biting and hitting her in her bed, and then hauled her out of her apartment before she freed herself, police say.
The woman ran to a parking lot and jumped into a car being driven by a neighbor. Bensley banged on the car window briefly before it sped away.
"I'm a vampire and I've been alive for over 500 years," Bensley said, Galveston Officer Daniel Erickson told the Houston Chronicle.
"He was begging us to restrain him because he didn't want to kill us," Erickson said. "He said he needed to feed."
Erickson said Bensley did not appear to be under the influence of drugs.
Bensley's bail has been set at $40,000.
