Many deep learning (DL)-based image restoration methods for low-dose CT (LDCT) problems directly employ the end-to-end networks on low-dose training data without considering dose differences. However, the radiation dose difference has a great impact on the ultimate results, and lower doses increase the difficulty of restoration. Moreover, there is increasing demand to design and estimate acceptable scanning doses for patients in clinical practice, necessitating dose-aware networks embedded with adaptive dose estimation. In this paper, we consider these dose differences of input LDCT images and propose an adaptive dose-aware network. First, considering a large dose distribution range for simulation convenience, we coarsely define five dose levels in advance as lowest, lower, mild, higher and highest radiation dose levels. Instead of directly building the end-to-end mapping function between LDCT images and high-dose CT counterparts, the dose level is primarily estimated in the first stage. In the second stage, the adaptively learned low-dose level is used to guide the image restoration process as the pattern of prior information through the channel feature transform. We conduct experiments on a simulated dataset based on original high dose parts of American Association of Physicists in Medicine challenge datasets from the Mayo Clinic. Ablation studies validate the effectiveness of the dose-level estimation, and the experimental results show that our method is superior to several other DL-based methods. Specifically, our method provides obviously better performance in terms of the peak signal-to-noise ratio and visual quality reflected in subjective scores. Due to the dual-stage process, our method may suffer limitations under more parameters and coarse dose-level definitions, and thus, further improvements in clinical practical applications with different CT equipment vendors are planned in future work.