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Mode coupling is an important mechanism to excite Alfvén waves and has been extensively investigated based on numerical simulations. However, no direct observational evidence has been found regarding to this mechanism in the magnetotail lobe. Here, we report an in-situ observation that an Alfvén wave with a period of several minutes is clearly relevant to a fast mode wave in the magnetotail lobe based on observations of the Cluster spacecraft. These waves occur at the region where the Alfvén speed has a gradient during an enhancement of the solar wind dynamic pressure. This suggests that the Alfvén wave is generated by the mode conversion at the region where the Alfvén speed has a gradient, and the fast mode wave might be driven by the solar wind. Our observations provide an important insight into the wave generation and energy conversion in the magnetosphere.