  We study a non-Hermitian Aubry-Andr\'e-Harper model with both nonreciprocal
hoppings and complex quasiperiodical potentials, which is a typical
non-Hermitian quasicrystal. We introduce boundary-dependent self-dualities in
this model and obtain analytical results to describe its Asymmetrical Anderson
localization and topological phase transitions. We find that the Anderson
localization is not necessarily in accordance with the topological phase
transitions, which are characteristics of localization of states and topology
of energy spectrum respectively. Furthermore, in the localized phase,
single-particle states are asymmetrically localized due to non-Hermitian skin
effect and have energy-independent localization lengths. We also discuss
possible experimental detections of our results in electric circuits.
