Due to the large number of hazardous materials and serious accident consequences, it has been attracting continuous attentions in the abnormal detection of the chemical plant. Although many detection methods are proposed in the literature, the actual anomaly detection is subject to two challenges. On the one hand, the advanced distributed control system (DCS) can provide massive information about the real-time operating statue of the device, but it also results in a high-order features of training dataset. On the other hand, there is scarce abnormal data in the establishment of abnormal training samples along with the continuous improving device reliability. As a response, this work proposes a PCA-SVDD-based abnormal condition detection method in chemical process under no abnormal data by combing principal component analysis (PCA) and support vector data description (SVDD). Firstly, PCA is employed to reduce the dimensionality by decomposing training samples, which consist of normal data, into the principal subspace and the residual subspace. Then, according to the target type data, an anomaly detection model based on SVDD is established. Further, the Gaussian kernel function is introduced to improve the anomaly detection effect. Finally, the normal data in Tennessee-Eastman (TE) process data is used as training samples to validate the PCA-SVDD. And the two indicators of detection precision (DP) and detection time (DT) are employed to characterize the effect of detection model. In contrast, traditional PCA and SVDD is introduced to carry on anomaly detection of TE process under the same condition. By the comparison, it concludes that the PCA-SVDD-based abnormal condition detection method proposed in this work has better detection effect (higher accuracy and less detection time). In summary, PCA-SVDD can realize the early warning of abnormal working conditions without abnormal data in the chemical process, and has certain significance to ensure the smooth operation of the device.