This paper examined both experimental and a new modelling test for biogas production based on Co-Digestion Ratio (CDR) of vegetable peel (VP) with cow dung (CD) without external inoculum. For this, vegetable peel was used as a substrate and cow dung was used as a co-substrate. Reactors in triplicate were prepared. The vegetable peel concentrations were 12, 8, 6 and 4 g VS/l with the same cow dung concentration (4 g of VS/l) which corresponds to a CDR of 3:1, 2:1, 1.5:1 and 1:1. A new mathematical model corresponding to the biotech anaerobic digestion process based only on the (CDR) and (VS) was implemented under Matlab Simulink. The experimental results indicate that the optimal cumulative methane production (CMP) of 2000 ml was generated in the reactor containing a (CDR) of 3:1 which corresponds to a methane yield of 170 ml CH4/ g VS. i.e., an improvement between 23 and 26% comparing to all other CDRs. The experimental results were conformed by the new mathematical model. After applying the invented new idea by converting the constants (Rm, L and Gm) into functions (Rm =f1 (CDR), L=f2(CDR) and Gm = f3 (VS)) and relating them to each other using the Gompertz relation. The new model was able to predict the methane produced using only two inputs: VS and CDR. While in the literature studies, which were used Gompertz relationship for kinetic modelling, the constants must be recalculated each time as a new model, although the substrates used are the same, only the composition is different. Analysis of the variance (ANOVA) between the experimental and modelling results showed that there is no statistically significant difference, with a significance level of 0.05. Finally, the invented new idea can be a key to another different research that uses the same substrate.