Based on the analysis of completeness and finiteness of HF molecular vibrational levels, HF systemic vibrational heat capacity is studied with quantum statistical and full set of vibrational energy level determined AM (algebraic method). The results show that correct vibrational description and vibrational energy level set of HF system are key factors in calculating heat capacity, HF heat capacity data determined by AM energy spectra {Eυ} are much superior to the ones of harmonic oscillator model, AM results are agreement with experiment data.