A new method for attenuation correction in positron computed tomography (PCT) was developed, and it can improve the quality of PCT images. The method requires a short transmission scan by the PCT system. Then boundaries between tissues with significantly different attenuation coefficients are determined from the transmission image by edge-finding techniques. Attenuation correction factors (ACF) are then calculated using these boundaries and the average attenuation coefficients within the enclosed regions. The method was tested on computer-simulated data, on scans of phantoms, and on patient studies, and was found effective in reducing the random noise in transmission measurements and in providing more accurate ACF than the method using geometric attenuation correction. As a result, transmission scan times can be shortened, inconvenience to patients is reduced, and PCT images are improved.