A new method for attenuation correction in positron computed tomography (PCT) has been 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 has been tested on computer-simulated data, on scans of phantoms, and on patient studies, and has been found effective in reducing the random noise in transmission measurements and in providing more accurate ACFs 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.