Tool wear monitoring (TWM) is of great importance for improving the machining quality and the efficiency of the milling process. Extracting a discriminative tool wear feature is the key to TWM. Cutting force coefficients, which reflect the tool–chip and tool–material contact form, are good indicators of tool wear condition. However, in the existing studies, only the tangential and radial cutting force coefficients are adopted to monitor tool wear. The axial coefficients extracted from the axial cutting force are neglected. Preliminary experiments have shown that, although the axial cutting force has a small amplitude, the axial cutting force coefficients are very discriminative regarding the tool wear condition. Fusing the axial coefficients and the traditional tangential and radial coefficients can improve the monitoring accuracy. Based on such a consideration, this study proposes a milling tool wear monitoring method in which the multichannel cutting force coefficients, viz., the tangential, radial, and axial cutting force coefficients, are fused to indicate the tool wear. A long short-term memory (LSTM) network is adopted to sequentially estimate the progressive tool wear value from the multichannel cutting force coefficients. The effectiveness of the proposed monitoring method is examined using the PHM 2010 data. The results show that the proposed method outperforms the traditional method. With the fusion of the multichannel coefficients, the monitoring accuracy improves by 2.74–6.35%.