The central nervous system (CNS) is made up of neurons and glial cells. Information is transmitted along axons to other neurons, muscles, or glands. Recent studies indicate possible changes in axon diameter distributions associated with diseases such as Alzheimer’s disease, autism, dyslexia, and schizophrenia. Magnetic resonance imaging (MRI) techniques such as diffusion MRI can be used to probe the tissue microstructure of the brain noninvasively. Current MRI axon diameter measurements rely on the pulsed gradient spin echo sequence which cannot provide short enough diffusion times to measure small axon diameters. Recent advances have allowed oscillating gradient (OG) diffusion MRI to infer the sizes of micron-scale axon diameters. Monte Carlo simulations of cosine OG sequences were conducted on a parallel cylinder (diameters 1 to 10 µm) geometry. For feasible experiments on a Bruker BG6 gradient set, the simulations inferred diameters as small as 1 µm on square packed and randomly packed cylinders. The accuracy of the inferred diameters was found to be dependent on the signal-to-noise ratio (SNR) with smaller diameters more affected by noise although all diameter distributions were distinguishable from one another for all SNRs tested. Five frequencies were adequate for d = 3 – 5 µm with single-sized cylinders and for effective mean axon diameters (AxD) greater than 2 µm for cylinders with a distributions of diameters. There was some improvement in precision for d = 1 – 2 µm with 10 frequencies. It was better to repeat measurements at higher gradient strengths than to use a range of gradient strengths. Data were collected from a portion of normal-appearing corpus callosum from an autopsy human brain, which did not demonstrate any pathological changes. The average fitted AxD was 2.0 ± 0.2 µm, while AxD obtained from electron microscopy was 1.4 ± 0.2 µm. Fitted AxD showed more variability below 7 OG frequencies and little change when using two or three gradient strengths, agreeing with the simulations.