Exchange biased nanostructures of IrMn/CoFe were deposited on anodized alumina with hexagonally patterned nanodot surface structures. Nanodots with diameters of 20, 70, and 100 nm were fabricated to investigate the size effect on the magnetic properties. Magnetometry and the first-order reversal curve method revealed significant enhancements of the exchange bias and coercivity in the nanodots compared with flat films. The enhancements can be attributed to the effective reduction of ferromagnet domain sizes and increased random fields due to the nanostructure morphology and domain wall pinning by the boundaries between adjacent nanodots.