Abstract Objective. Positron emission tomography (PET) image reconstruction needs to be corrected for scatter in order to produce quantitatively accurate images. Scatter correction is traditionally achieved by incorporating an estimated scatter sinogram into the forward model during image reconstruction. Existing scatter estimated methods compromise between accuracy and computing time. Nowadays scatter estimation is routinely performed using single scatter simulation (SSS), which does not accurately model multiple scatter and scatter from outside the field-of-view, leading to reduced qualitative and quantitative PET reconstructed image accuracy. On the other side, Monte-Carlo (MC) methods provide a high precision, but are computationally expensive and time-consuming, even with recent progress in MC acceleration. Approach. In this work we explore the potential of deep learning (DL) for accurate scatter correction in PET imaging, accounting for all scatter coincidences. We propose a network based on a U-Net convolutional neural network architecture with 5 convolutional layers. The network takes as input the emission and computed tomography (CT)-derived attenuation factor (AF) sinograms and returns the estimated scatter sinogram. The network training was performed using MC simulated PET datasets. Multiple anthropomorphic extended cardiac-torso phantoms of two different regions (lung and pelvis) were created, considering three different body sizes and different levels of statistics. In addition, two patient datasets were used to assess the performance of the method in clinical practice. Main results. Our experiments showed that the accuracy of our method, namely DL-based scatter estimation (DLSE), was independent of the anatomical region (lungs or pelvis). They also showed that the DLSE-corrected images were similar to that reconstructed from scatter-free data and more accurate than SSS-corrected images. Significance. The proposed method is able to estimate scatter sinograms from emission and attenuation data. It has shown a better accuracy than the SSS, while being faster than MC scatter estimation methods.