The objective of the study was to examine the application of the Anaerobic Digestion Model No. 1 (ADM1) developed by the IWA task group for mathematical modelling of anaerobic process. Lab-scale temperature-phased anaerobic digestion (TPAD) process were operated continuously, and were fed with co-substrate composed of dog food and flour. The model platform implemented in the simulation was a derivative of the ADM1. Sensitivity analysis showed that k(m.process) (maximum specific uptake rate) and K(S.process) (half saturation value) had high sensitivities to model components. Important parameters including maximum uptake rate for propionate utilisers (k(m.pro)) and half saturation constant for acetate utilisers (K(S.ac)) in the thermophilic digester and maximum uptake rate for acetate utilisers (k(m.ac)) in the mesophilic digester were estimated using iterative methods, which optimized the parameters with experimental results. Simulation with estimated parameters showed good agreement with experimental results in the case of methane production, uptake of acetate, soluble chemical oxygen demand (SCOD) and total chemical oxygen demand (TCOD). Under these conditions, the model predicted reasonably well the dynamic behavior of the TPAD process for verifying the model.