Although in-orbit anomaly detection is extremely important to ensure spacecraft safety, the complex spatial-temporal correlation and sparsity of anomalies in the data pose significant challenges. This study proposes the new multi-task learning-based time series anomaly detection (MTAD) method, which captures the spatial-temporal correlation of the data to learn the generalized normal patterns and hence facilitates anomaly detection. First, four proxy tasks are implemented for feature extraction through joint learning: (1) Long short-term memory-based data prediction; (2) autoencoder-based latent representation learning and data reconstruction; (3) variational autoencoder-based latent representation learning and data reconstruction; and (4) joint latent representation-based data prediction. Proxy Tasks 1 and 4 capture the temporal correlation of the data by fusing the latent space, whereas Tasks 2 and 3 fully capture the spatial correlation of the data. The isolation forest algorithm then detects anomalies from the extracted features. Application to a real spacecraft dataset reveals the superiority of our method over existing techniques, and further ablation testing for each task proves the effectiveness of fusing multiple tasks. The proposed MTAD method demonstrates promising potential for effective in-orbit anomaly detection for spacecraft.