Respiratory motion results in significant motion blur in thoracic positron emission tomography (PET) imaging. Existing approaches to correct the blurring artifact involve acquiring the images in gated mode and using complicated reconstruction algorithms. In this paper, we propose a post-reconstruction framework to estimate respiratory motion and reduce the motion blur of PET images acquired in ungated mode. Our method includes two steps: one is to use minmax directional derivative analysis and local auto-correlation analysis to identify the two parameters blur direction and blur extent, respectively, and another is to employ WRL, à trous wavelet-denoising modified Richardson-Lucy (RL) deconvolution, to reduce the motion blur based on identified parameters. The mobile phantom data were first used to test the method before it was applied to 32 cases of clinical lung tumor PET data. Results showed that the blur extent of phantom images in different directions was accurately identified, and WRL can remove the majority of motion blur within ten iterations. The blur extent of clinical images was estimated to be 12.1 ± 3.7 mm in the direction of 74 ± 3° relative to the image horizontal axis. The quality of clinical images was significantly improved, both from visual inspection and quantitative evaluation after deconvolution. It was demonstrated that WRL outperforms RL and a Wiener filter in reducing the motion blur with one to two more iterations. The proposed method is easy to implement and thus could be a useful tool to reduce the effect of respiration in ungated thoracic PET imaging.