A task-oriented over-the-air computation (AirComp) scheme is proposed in this paper for multi-device edge split inference system. In the considered system, local noise-corrupted feature vectors are aggregated at the server via AirComp to generate a denoised one for the subsequent inference task. By considering classification tasks, the transmit precoders at edge devices and receive beamforming at edge server are jointly designed in an effort to rein in the aggregation error and maximize the inference accuracy, which is approximately measured by a surrogate but more tractable metric called discriminant gain. It is found that the conventional AirComp beamforming design for minimizing the mean square error between the aggregated feature vector by AirComp and the ideally aggregated one may not lead to the optimal classification accuracy, as it fails to respect the fact that some feature dimensions are more sensitive to the aggregation error than the others in terms of the classification accuracy. To tackle this issue, a new task-oriented AirComp scheme is proposed for directly maximizing the derived discriminant gain. The superiority of the proposed scheme over the heuristic benchmarks is verified by extensive experimental results based on a concrete inference task of human motion recognition.