Yes, both. Humans (Homo sapiens) are vertebrates because we have a backbone, or vertebral column, that surrounds and protects the spinal cord, plus a skull (cranium) that protects the brain.
Humans are also mammals: like other members of class Mammalia, we have hair, are warm-blooded, and feed our young milk from mammary glands. Within the mammals, humans belong to the primate order.
Source: Wikipedia: Vertebrate