In this paper, a new type of 3D bin packing problem (BPP) is proposed, in which a number of cuboidshaped items must be put into a bin one by one orthogonally. The objective is to find a way to place these items that can minimize the surface area of the bin. This problem is based on the fact that there is no fixed-sized bin in many real business scenarios and the cost of a bin is proportional to its surface area. Our research shows that this problem is NP-hard. Based on previous research on 3D BPP, the surface area is determined by the sequence, spatial locations and orientations of items. Among these factors, the sequence of items plays a key role in minimizing the surface area. Inspired by recent achievements of deep reinforcement learning (DRL) techniques, especially Pointer Network, on combinatorial optimization problems such as TSP, a DRL-based method is applied to optimize the sequence of items to be packed into the bin. Numerical results show that the method proposed in this paper achieve about 5% improvement than heuristic method.