A new iterative reconstruction technique (NIRT) for positron emission computed tomography (PET), which uses transmission data for nonuniform attenuation correction, is described. Utilizing the general inverse problem theory, a cost functional which includes a noise term was derived. The cost functional was minimized using a weighted-least-square maximum a posteriori conjugate gradient (CG) method. The procedure involves a change in the Hessian of the cost function by adding an additional term. Two phantoms were used in a real data acquisition. The first was a cylinder phantom filled with uniformly distributed activity of 74 MBq of fluorine-18. Two different inserts were placed in the phantom. The second was a Hoffman brain phantom filled with uniformly distributed activity of 7.4 MBq of 18F. Resulting reconstructed images were used to test and compare a new iterative reconstruction technique with a standard filtered backprojection (FBP) method. The results confirmed that NIRT, based on the conjugate gradient method, converges rapidly and provides good reconstructed images. In comparison with standard results obtained by the FBP method, the images reconstructed by NIRT showed better noise properties. The noise was measured as rms% noise and was less, by a factor of 1.75, in images reconstructed by NIRT than in the same images reconstructed by FBP. The distance between the Hoffman brain slice reconstructed by FBP and the perfect PET Hoffman brain slice created from the MRI image was 0.526, while the same distance for the Hoffman brain slice reconstructed by NIRT was 0.328. The NIRT method suppressed the propagation of the noise without visible loss of resolution in the reconstructed PET images.