This paper proposes an automatic stream-weight optimization method for noise-robust speaker verification using multi-stream HMMs integrating spectral and prosodic information. The paper first shows the effectiveness of the multi-stream technique in our speaker verification framework. Next, a stream-weight adaptation method combining the linear discriminant analysis (LDA) and Adaboost techniques is proposed. Experiments were conducted using four-connected-digit utterances of Japanese contaminated by white noise with various SNRs. Experimental results show that 1) the verification performance was improved in all SNR conditions by using stream weights estimated by the LDA and 2) the performance is further improved by using the Adaboost in 10 - 30dB SNR conditions.