Considering that the demand requirements are fuzzy demand in each period during the planning horizon, this paper focuses on a novel approach to modelling multi-product aggregate production planning (APP) problems with fuzzy demands and fuzzy capacities. The objective of the problem considered is to minimize the total costs of quadratic production costs and linear inventory holding costs. By means of formulation of fuzzy demand, fuzzy addition and fuzzy equation, the productioninventory balance equation in single stage and dynamic balance equation are formulated as soft equations in terms of a degree of truth, and interpreted as the levels of satisfaction with production and inventory plan in meeting market demands. As a result, the multi-product aggregate production planning problem with fuzzy demands and fuzzy capacities can be modelled into a fuzzy quadratic programming with fuzzy objective and fuzzy constraints. The fuzzy solution approach to the model is also proposed in this paper. It can offer the decision-maker (DM) more choices to construct an aggregate production plan so as to ensure the feasibility of family disaggregation plan, especially in fuzzy environment.