Integrated nonlinear photonic circuits received rapid development in recent years, providing all-optical functionalities enabled by cavity-enhanced photon-photon interaction for classical and quantum applications. A high-efficiency fiber-to-chip interface is key to the use of these integrated photonic circuits for quantum information tasks, as photon loss is a major source that weakens quantum protocols. Here, overcoming material and fabrication limitation of thin-film aluminum nitride by adopting a stepwise waveguiding scheme, we demonstrate low-loss adiabatic fiber-optic couplers in aluminum nitride films with a substantial thickness (600 nm) for optimized nonlinear photon interaction. For telecom (1550 nm) and near-visible (780 nm) transverse magnetic-polarized light, the measured insertion loss of the fiber-optic coupler is -0.97 dB and -2.6 dB, respectively. Our results will facilitate the use of aluminum nitride integrated photonic circuits as efficient quantum resources for generation of entangled photons and squeezed light on microchips.