Summary: Arithmetic coding is a powerful lossless data compression technique that has attracted much attention in recent years. It provides more flexibility and better efficiency than Huffman coding does. However, the multiplications needed in its encoding and decoding algorithms are very undesirable. \textit{J. Rissanen} and \textit{K. M. Mohiuddin} [IEEE Trans. Commun. 37, 93-98 (1989)] have proposed a simple scheme to avoid the multiplications. We found that the performance of their proposed scheme might degrade significantly in some cases. In this paper, we propose a multiplication-free multialphabet arithmetic code which can be shown to have minor performance degradation in all cases. In our proposed scheme, each multiplication is replaced by a single shift-and-add. We will prove, by both theoretical analysis and simulation results, that the degradation of the proposed multiplication-free scheme is always several times (2-7 times in our experiments) smaller than that of the Rissanen-Mohiuddin's scheme.