The improper management of goat manure from concentrated goat feeding operations and food waste leads to the emission of greenhouse gasses and water pollution in the US. The wastes were collected from the International Goat Research Center and a dining facility at Prairie View A&M University. The biochemical methane potential of these two substrates in mono and co-digestion at varied proportions was determined in triplicates and processes were evaluated using two nonlinear regression models. The experiments were conducted at 36 ± 1 °C with an inoculum to substrate ratio of 2.0. The biomethane was measured by water displacement method (pH 10:30), absorbing carbon dioxide. The cumulative yields in goat manure and food waste mono-digestions were 169.7 and 206.0 mL/gVS, respectively. Among co-digestion, 60% goat manure achieved the highest biomethane yields of 380.5 mL/gVS. The biodegradabilities of 33.5 and 65.7% were observed in goat manure and food waste mono-digestions, while 97.4% were observed in the co-digestion having 60% goat manure. The modified Gompertz model is an excellent fit in simulating the anaerobic digestion of food waste and goat manure substrates. These findings provide useful insights into the co-digestion of these substrates.