The global shift towards diets high in sugar-sweetened beverages (SSBs) is linked to higher prevalence of obesity, diabetes and most other non-communicable diseases. In Colombia, one out of every two people was overweight or obese by 2010. This study estimates price-elasticities from a Quadratic Almost Ideal Demand System model, using the 2006–2007 Colombian Income and Expenditure survey. The food groups that were jointly considered were: unsweetened unflavored milks; coffee and tea; sugar sweetened beverages (SSBs); sweets and candies (including sugar); dairy products; meats and animal-based products; grains based staples; fruits and vegetables; and condiments and snacks. We take into account the high proportion of households not purchasing specific food and beverage groups (censored data) and endogeneity on both prices (as unit values) and total expenditure. Unhealthy beverages are price-elastic (-1.61 for SSBs) meaning that the change in consumption is proportionally larger with respect to a change in price. Also, there is a high complementarity among SSBs and major food groups (grains, meats and fruits and vegetables). In Colombia, the design of a meaningful tax to influence healthier diets is a next critical step. This study also shows that a tax of 20% on SSBs should prove to be effective, and can yield revenues of about 1% of the Colombian government’s total annual fiscal revenue, which can potentially be directed towards public health promotion and investments.