This article discusses the relevance of in situ quality assurance in metal additive manufacturing for cost-efficient product qualification. It presents an approach for monitoring the laser powder bed fusion (LPBF) process using an area-scan hyperspectral camera to predict the surface roughness Rzwith the help of a convolutional neural network. These investigations were carried out during LPBF processing of the magnesium alloy WE43 that, due to its bioresorbability and compatibility, holds significant potential for biomedical implants. A data acquisition and processing methodology has been set up to enable efficient management of the hyperspectral data. The hyperspectral images obtained from the process were labeled with the surface roughness Rzas determined by a confocal microscope. The data was used to train a convolutional neural network whose hyperparameters were optimized in a hyperparameter tuning process. The resulting network was able to predict the surface roughness within a mean absolute error (MAE) of 4.1μm over samples from three different parameter sets. Since this is significantly smaller than the spread of the actual roughness measured (MAE = 14.3μm), it indicates that the network identified features in the hyperspectral data linking to the roughness. These results provide the basis for future research aiming to link hyperspectral process images to further part properties relevant for quality assurance.