To address the heavy-tailed, spike-prone nature of sea clutter and the scarcity of labeled target data, an unsupervised complex-valued variational autoencoder (VAE) for maritime radar target detection is proposed. In implementation, each complex baseband slow-time sequence is represented by its in-phase and quadrature components, and the model learns their joint reconstruction from clutter-only data. A Student-\(t\) negative log-likelihood is adopted to capture heavy-tailed reconstruction errors while reducing sensitivity to outliers during clutter learning. In addition, a time-domain amplitude error constraint is introduced to penalize slow-time magnitude mismatch in the reconstruction. At inference, reconstruction deviation is used as the detection statistic, and the decision threshold is set via an empirical quantile estimated from a clutter-only validation set to enforce a constant false-alarm rate (CFAR). Experiments on measured sea-clutter data show that detection performance is consistently improved over MF, AMF, and a real-valued \(β\)-VAE under CFAR constraints.