In this paper, we present two approaches to improve the eigenvoice-based speaker adaptation. First, we present the maximum a posteriori eigen-decomposition (MAPED), where the linear combination coefficients for eigenvector decomposition are estimated according to the MAP criterion. By incorporating the prior decomposition knowledge, here we use a Gaussian distribution, the MAPED is established accordingly. MAPED is able to achieve better performance than maximum likelihood eigen-decomposition (MLED) with few adaptation data. On the other hand, we exploit the adaptation of covariance matrices of the hidden Markov model (HMM) in the eigenvoice framework. Our method is to use the principal component analysis (PCA) to project the speaker-specific HMM parameters onto a smaller orthogonal feature space. Then, we reliably calculate the HMM covariance matrices using the observations in the reduced feature space. The adapted HMM covariance matrices are estimated by transforming the covariance matrices in the reduced feature space to that in the original feature space. The experimental results show that the eigenvoice speaker adaptation using MAPED and incorporating covariance adaptation can improve the performance of the original eigenvoice adaptation in Mandarin speech recognition.