This research develops a food demand system model based on the Linear Almost Ideal Demand System (LA/AIDS). The major contribution of this research is that the opportunity cost of time on food cooking/cleaning up is modeled in the demand system. Different from the traditional one constraint demand, this two constraints LA/AIDS model better captures consumer behavior and attitude toward food choice –food at home (FAH), sugar sweetened beverage (SSB), food away from home (FAFH). Using Statistics Canada Food Expenditure Survey (FES) and General Social Survey-time use, a two sample two stage least square (2S2SLS) is an applied in the data estimation. The empirical results show most coefficient estimates and own price elasticities are significant. FAH and FAFH are found to be more price elastic compared to a one constraint model, and SSB is found to be more price inelastic. This research provides a new perspective to estimate potential food policies, such as, a tax on SSB, or a food tax on "junk food".