X-ray computed tomography (CT) and positron emission tomography (PET) are two of the most commonly used medical imaging technologies for the evaluation of many diseases. Full-dose imaging for CT and PET ensures the image quality but usually raises concerns about the potential health risks of radiation exposure. The contradiction between reducing the radiation exposure and remaining diagnostic performance can be addressed effectively by reconstructing the low-dose CT (L-CT) and low-dose PET (L-PET) images to the same high-quality ones as full-dose (F-CT and F-PET). In this paper, we propose an Attention-encoding Integrated Generative Adversarial Network (AIGAN) to achieve efficient and universal full-dose reconstruction for L-CT and L-PET images. AIGAN consists of three modules: the cascade generator, the dual-scale discriminator and the multi-scale spatial fusion module (MSFM). A sequence of consecutive L-CT (L-PET) slices is first fed into the cascade generator that integrates with a generation-encoding-generation pipeline. The generator plays the zero-sum game with the dual-scale discriminator for two stages: the coarse and fine stages. In both stages, the generator generates the estimated F-CT (F-PET) images as like the original F-CT (F-PET) images as possible. After the fine stage, the estimated fine full-dose images are then fed into the MSFM, which fully explores the inter- and intra-slice structural information, to output the final generated full-dose images. Experimental results show that the proposed AIGAN achieves the state-of-the-art performances on commonly used metrics and satisfies the reconstruction needs for clinical standards.