The aim of this study was to examine the size and geometry of the capillary network in tuna red muscle, one of the most aerobic muscles in fish. Deep red muscle of 1.5- to 2-kg skipjack tuna, Katsuwonus pelamis, was perfusion fixed in situ, processed for electron microscopy, and analyzed by morphometry. Fiber cross-sectional area was 560 ± 30 (SE) μm2 in the samples. Capillary length per fiber volume was 4143 ± 242 (SE) mm−2 and mitochondrial volume density 28.5 ± 1.0 (SE) %. Indexes of capillarity such as average number of capillaries around a fiber, capillary length and surface per fiber volume, and capillary surface per fiber surface were high for a fish muscle. In fact, the size of the capillary–fiber interface (i.e., capillary to fiber surface) at a given mitochondrial volume per fiber was not significantly different in tuna red muscle compared with rat soleus muscle. However, calculation of mitochondrial respiratory rates in tuna red muscle yielded a substantially lower value (approximately 1/20th) compared with muscles of mammals. Besides the possible effect of differences in operating temperatures and (or) mitochondrial function(s) in fish compared with mammals, this suggests that the large capillary–fiber interface in tuna may be related to functions other than oxygen delivery per se, such as substrate and (or) heat transfer between capillaries and muscle fiber.