Abstract KLiSO4 of the P63 symmetry is a well refined crystal at room temperature, which is a pyroelectric material with a large second harmonic generation response. However, its fundamental physical properties are still not well studied. In this work, first principles calculations are performed to study its electronic, optical, elastic, piezoelectric and vibrational properties. The results indicate that it is an ionic crystal with a large indirect band gap. Calculated optical properties imply that P63 KLiSO4 has little optical anisotropy at low frequencies. Obtained elastic constants reveal that it is mechanically stable but anisotropic, as illustrated by the directional bulk and shear moduli. Piezoelectric coefficients, dielectric constants, and Born effective charges (BECs) are computed using the density functional perturbation method. Studies disclose that it has a greater piezoelectric coefficient along the c axis. The ions have more contribution to the total dielectric constants than the electrons. The S atoms have the largest BECs. The phonon vibrational modes at the Brillouin zone center are analyzed by the factor group theory. Its infrared and Raman spectra are simulated. The causation for the vanishment of some infrared peaks in the computed infrared spectrum is uncovered. Additionally, elastic related moduli, hardness, melting point and electromechanical coupling coefficients of P63 KLiSO4 are also predicated.