While Swedish last names often have the "-son" or "-sson" suffix, "Mellquist" doesn't follow that pattern. Furthermore, a quick search of Swedish genealogy databases and name dictionaries doesn't reveal "Mellquist" as a common or known surname.
It's possible that "Mellquist" might be a variation of a Swedish name, or a name from another language entirely. Without more context, it's difficult to determine its origin.