This paper presents a new method of feature dimension reduction in hidden Markov modeling (HMM) for speech recognition. The key idea is to apply reduced rank maximum likelihood estimation in the M-step of the usual Baum-Welch algorithm for estimating HMM parameters such that the estimates of the Gaussian distribution parameters are restricted in a sub-space of reduced dimensionality. There are two main advantages of applying this method in HMM: 1) feature dimension reduction is achieved simultaneously with the estimation of HMM parameters, therefore it guarantees that the likelihood function is monotonically increasing; 2) it requires very little extra computation in addition to the standard Baum-Welch algorithm, hence it can be easily incorporated in the existing speech recognition systems using HMMs.