That computer has an AMD CPU in it right? If it does, yes that videocard can work with it IF:
The case has enough space. Some HP computers might be small form factors which accept only low profile cards, or possibly no card at all.
The power supply can handle it. Some HP computers might have lower powered power supplies which can't power a videocard.
The motherboard supplies the standard 75W on the pci-ex slot. Some HPs might use non standard motherboards which don't put out enough power.
Since you provided no computer model number I can't say exactly what your options are.