With the increasing demand for high quality audio, stereo audio coding has become more and more important. In this paper, a multi-frame coding method based on Principal Component Analysis (PCA) is proposed for the compression of audio signals, including both mono and stereo signals. The PCA-based method makes the input audio spectral coefficients into eigenvectors of covariance matrices and reduces coding bitrate by grouping such eigenvectors into fewer number of vectors. The multi-frame joint technique makes the PCA-based method more efficient and feasible. This paper also proposes a quantization method that utilizes Pyramid Vector Quantization (PVQ) to quantize the PCA matrices proposed in this paper with few bits. Parametric coding algorithms are also employed with PCA to ensure the high efficiency of the proposed audio codec. Subjective listening tests with Multiple Stimuli with Hidden Reference and Anchor (MUSHRA) have shown that the proposed PCA-based coding method is efficient at processing stereo audio.