PET enables quantitative imaging of the rate constants K1, k2, k3, and k4, with a reversible two tissue compartment model (2TCM). A new method is proposed for computing all of these rates within a reasonable time, less than 1 min. A set of differential equations for the reversible 2TCM was converted into a single formula consisting of differential and convolution terms. The validity was tested on clinical data with 18F-FLT PET for patients with glioma (n = 39). Parametric images were generated with the formula that was developed. Parametric values were extracted from regions of interest (ROIs) for glioma from the images generated, and they were compared with those obtained with the non-linear fitting method. We performed simulation studies for testing accuracy by generating simulated images, assuming clinically expected ranges of the parametric values. The computation time was about 20 s, and the quality of the images generated was acceptable. The values obtained for K1for grade IV tumor were 0.24 ± 0.23 and 0.26 ± 0.25 ml−1 min−1 g−1for the image-based and ROI-based methods, respectively. The values were 0.21 ± 0.12 and 0.21 ± 0.12 min−1for k2, 0.13 ± 0.07 and 0.13 ± 0.07 min−1for k3, and 0.052 ± 0.020 and 0.054 ± 0.021 min−1for k4. The differences between the methods were not significant. Regression analysis showed correlations of r = 0.94, 0.86, 0.71, and 0.52 for these parameters. Simulation demonstrated that the accuracy was within acceptable ranges, namely, the correlations were r = 0.99, r = 0.97, r = 0.99, and r = 0.91 for K1, k2, k3, and k4, respectively, between estimated and assumed values. This results suggest that parametric images can be obtained fully within reasonable time, accuracy, and quality.