A fuzzy combined linear regression model for fuzzy initial data, which are tolerant (L-R)-numbers with constraints on the functions L and R, is designed. The model is called combined since it is a combination of two regression models—a fuzzy model and a classical model. Its coefficients are determined as unimodal (L-R)-numbers. The solution method consists in determining weighted intervals for the tolerant (L-R)-numbers and then applying of the least-squares method.