The multi-attribute decision making problems that the attribute weights (interval numbers) are partly known and the attribute values are numeric are investigated. Firstly, based on the optimal overall attribute values of alternatives in local and whole, two goal-programming models are established, respectively. Secondly, the ranking priorities on alternatives are obtained by solving the two models. A novel method based on two-phase goal programming model for multi-attribute decision-making is proposed. The method is characterized by simple operation and easy to implement on computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed model and method.