Pulmonary Embolism (PE) is a common and serious disease. Indeed, the annual incidence is 1/1000 patients per year and the 3-month mortality is 10%, which is twice that of myocardial infarction. The treatment is based on anticoagulation for at least 3 months. However, after three or six months of anticoagulation, persistent dyspnea and impairment of quality of life are observed in at least 30% of cases. Several mechanisms explain dyspnea and impairment of quality of life after PE, such as residual pulmonary artery obstruction, exercise deconditioning, depressive syndrome or development of a cardio-respiratory pathology. Pulmonary rehabilitation (PR) has been shown to be effective on dyspnea and quality of life and is included in the therapeutic management of chronic respiratory diseases such as Chronic Obstructive Pulmonary Disease (COPD) or pulmonary fibrosis. Furthermore, PR is also used after a myocardial infarction. However, PR after PE is still not included in therapeutic management of PE while outpatient management is recommended for the majority of patients after an acute PE episode. Study hypothesis is that PR has the potential to improve quality of life and dyspnea perception in patients who have received anticoagulation for at least 3 months after PE and who present an impairment of quality of life and/or a persistent dyspnea. This study presents several innovative aspects. First, to our knowledge, This study is the first large randomized trial assessing PR at least 3 months after acute symptomatic PE. Only one small randomized trial on 18 patients evaluating the impact of PR after PE has been published; as PR was performed just after the acute phase of PE in this trial, the clinical status improvement observed in this study could not be explained by PR alone, but also by anticoagulation. In this study, the investigators will include 112 patients at least 3 months after PE in order to exclude the bias related to anticoagulation effect. Second, This study is the first large randomized trial. Third, this study is the first that have the potential to demonstrate efficacy and safety of delayed PR after PE in patients with impaired quality of life due to persistent residual dyspnea.