We present a noise adaptive speech recognition approach, where time-varying noise parameter estimation and Viterbi process are combined together. The Viterbi process provides approximated joint likelihood of active partial paths and observation sequence given the noise parameter sequence estimated till previous frame. The joint likelihood after normalization provides approximation to the posterior probabilities of state sequences for an EM-type recursive process based on the sequential Kullback proximal algorithm to estimate the current noise parameter. The combined process can easily be applied to perform continuous speech recognition in presence of non-stationary noise. Experiments were conducted in simulated and real non-stationary noises. Results showed that the noise adaptive system provides significant improvements in word accuracy as compared to the baseline system (without noise compensation) and the normal noise compensation system (which assumes the noise to be stationary).