Background The development of deep neural networks is facilitating more advanced digital analysis of histopathologic images. We trained a convolutional neural network for multiclass segmentation of digitized kidney tissue sections stained with periodic acid-Schiff (PAS). Methods We trained the network using multiclass annotations from 40 whole-slide images of stained kidney transplant biopsies and applied it to four independent data sets. We assessed multiclass segmentation performance by calculating Dice coefficients for ten tissue classes on ten transplant biopsies from the Radboud University Medical Center in Nijmegen, The Netherlands, and on ten transplant biopsies from an external center for validation. We also fully segmented 15 nephrectomy samples and calculated the networks glomerular detection rates and compared network-based measures with visually scored histologic components (Banff classification) in 82 kidney transplant biopsies. Results The weighted mean Dice coefficients of all classes were 0.80 and 0.84 in ten kidney transplant biopsies from the Radboud center and the external center, respectively. The best segmented class was "glomeruli" in both data sets (Dice coefficients, 0.95 and 0.94, respectively), followed by "tubuli combined" and "interstitium." The network detected 92.7% of all glomeruli in nephrectomy samples, with 10.4% false positives. In whole transplant biopsies, the mean intraclass correlation coefficient for glomerular counting performed by pathologists versus the network was 0.94. We found significant correlations between visually scored histologic components and network-based measures. Conclusions This study presents the first convolutional neural network for multiclass segmentation of PAS-stained nephrectomy samples and transplant biopsies. Our network may have utility for quantitative studies involving kidney histopathology across centers and provide opportunities for deep learning applications in routine diagnostics.