In this paper, we consider the hidden Markov model(HMM) parameter compensation in noisy environments with multiple noise sources based on the vector Taylor series (VTS) approach. General formulations for multiple environmental variables are derived and systematic expectation-maximization (EM) solutions are presented in maximum likelihood (ML) sense. It is assumed that each noise source is independent and having Gaussian distribution. To evaluate proposed method, we conduct speaker independent isolated word recognition experiments in various noisy environments. Experimental results show that proposed algorithm ahieves significant improvement. Especially, the proposed method is consistently more effective than the parallel model combination (PMC) based on log-normal approximation.