HIV carries the enzyme reverse transcriptase, which it uses to convert its RNA genome into DNA before that DNA gets inserted into the host cell's own chromosome. This reverse flow of information, from RNA back to DNA, is the hallmark of the retrovirus family (Retroviridae), and HIV is the best-known human example. So while HIV is technically also an RNA virus, the precise and complete classification asked for here is retrovirus.
We can also answer this by thinking about the word "retro" itself and what it implies about the direction of genetic information flow.
Since the reverse-transcription step is what uniquely defines HIV's replication strategy, the family name that captures this is retrovirus.
Therefore, the correct answer is Retrovirus.