Recent advances in information technology have led to the appearance of high‐dimensional and complex data sets which necessitates in‐depth investigation on high‐dimensional data analysis and modelling. The current study introduces five approaches to fit a functional linear regression model on interval‐valued functional data. The proposed approaches are based on the functional linear regression models on a sort of data where the response is an interval‐valued scalar random variable and the predictors are interval‐valued functional. In the first proposed method, a functional linear regression model is fitted based on the midpoints of the intervals. The second method involves two independent functional linear models on the midpoint and the half range of the intervals. Furthermore, the third method is based on a combination of the midpoint and the half range of intervals. In the fourth one, we formulate an interval‐valued functional predictor as a bivariate curve and introduce the bivariate functional linear regression model. Finally, the last method is based on Monte Carlo Markov Chain. The proposed methods are evaluated and compared through Monte Carlo simulation and real data analysis.