3D acquisition and reconstruction in positron emission tomography (PET) produce data with improved signal-to-noise ratios compared with conventional 2D slice-oriented methods. However, the sensitivity increase is accompanied by an increase in the number of scattered photons and random coincidences detected. This paper presents a scatter correction technique for 3D PET data where an estimate of the scattered photon distribution is subtracted from the data before reconstruction. The scatter distribution is estimated by iteratively convolving the photopeak projections with a mono-exponential kernel. The method accounts for the 3D acquisition geometry and nature of scatter by performing the scatter estimation on 2D projections. The assumptions of the method have been investigated by measuring the variation in the scatter fraction and the scatter function at different positions in a cylinder. Both parameters were found to vary by up to 50% from the centre to the edge of a large water-filled cylinder. Despite this, in a uniform cylinder containing water with different concentrations of radioactivity, scatter was reduced from 25% in a non-radioactive region to less than 5% using the convolution-subtraction method. In addition, the relative concentration of a cylinder containing an increased concentration, which was underestimated by almost 50% without scatter correction, was within 5% of the true concentration after correction.