Uncertainty plays an important role in predicting the future earning of the assets in the financial market and it is generally measured in terms of probability. But in some cases, it would be a good idea for an investor to state the expected returns on assets in the form of closed intervals. Therefore, in this paper, we consider a portfolio selection problem wherein expected return of any asset, risk level and proportion of total investment on assets are in the form of interval, and obtain an optimum (best) portfolio. Such portfolio gives the total expected return and proportion of total investment on assets in the form of interval. The proposed portfolio model is solved by considering an equivalent linear programming problem, where all the parameters of the objective function and constraints as well as decision variables are expressed in form of intervals. The procedure gives a strongly feasible optimal interval solution of such problem based on partial order relation between intervals. Efficacy of the results is demonstrated by means of numerical examples.