Summary: In this paper, we propose a new one-dimensional (1D) integer discrete cosine transform (Int-DCT) for unified lossless/lossy image compression. The proposed 1D Int-DCT is newly designed to reduce rounding effects by minimizing number of rounding operations. The proposed Int-DCT can be operated not only lossless coding for a high quality decoded image but also lossy coding for a compatibility with the conventional DCT-based coding system. Both theoretical analysis and simulation results confirm an effectiveness of the proposed Int-DCT.