Fc fusion proteins of human growth hormone with good biological activities relative to rhGH on a molar basis are disclosed. The hGH-L-vFc fusion protein comprises hGH, a flexible peptide linker of about 20 or fewer amino acids, and a human IgG Fc variant. The Fc variant is of a non-lytic nature and shows minimal undesirable Fc-mediated side effects. A method is also disclosed to make or produce such fusion proteins at high expression levels. Such hGH-L-vFc fusion proteins exhibit extended or prolonged serum half-life and/or good biological activities relative to that of rhGH on a molar basis, leading to improved pharmacokinetics and pharmacodynamics, thus fewer injections will be needed within a period of time.