Recently, deep learning-driven studies have been introduced for bioacoustic signal classification. Most of them, however, have the limitation that the input of the classifier needs to match with a trained label which is known as closed set recognition (CSR). To this end, the classifier trained by CSR would not cover a real stream task since the input of the classifier has so many variations. To combat real-world tasks, open set recognition (OSR) has been developed. In OSR, randomly collected inputs are fed to the classifier and the classifier predicts target classes and Unknown class. However, this OSR has been spotlighted in the studies of computer vision and speech domains while the domain of bioacoustic signal is less developed. Especially, to our best knowledge, OSR for animal sound classification has not been studied. This paper proposes a novel method for open set bioacoustic signal classification based on Class Anchored Clustering (CAC) loss with closed set unknown bioacoustic signals. To use the closed set unknown signals for training, a total of n +1 classes are used by adding one additional Unknown class to n target classes, and n +1 cross-entropy loss is added to the CAC loss. To evaluate the proposed method, we build an animal sound dataset that includes 101 species of sounds and compare its performance with baseline methods. In the experiments, our proposed method shows higher performance than other baseline methods in the area under the receiver operating curve for detecting target class and unknown class, the classification accuracy of open set signals, and classification accuracy for target classes. As a result, the closed set class samples are well classified while the open set unknown class can be also recognized with high accuracy at the same time.