  Mobility edge (ME), a critical energy separating localized and extended
states in spectrum, is a central concept in understanding the localization
physics. However, there are few models with exact MEs. In the paper, we
generalize the Aubry-Andr\'{e}-Harper model proposed in [Phys. Rev. Lett. 114,
146601 (2015)] and recently realized in [Phys. Rev. Lett. 126, 040603 (2021)],
by introducing a relative phase in the quasiperiodic potential. Applying
Avila's global theory we analytically compute localization lengths of all
single-particle states and determine the exact expression of ME, which both
significantly depend on the relative phase. They are verified by numerical
simulations, and a physical perception of the exact expression is also
provided. We further demonstrate that the exact expression of ME works for an
even broad class of generalized Aubry-Andr\'{e}-Harper models. Moreover, we
show that the exact ME is related to the one in the dual model which has
long-range hoppings.
