One of the main challenge in non-native speech recognition is how to handle acoustic variability present in multiaccented non-native speech with limited amount of training data. In this paper, we investigate an approach that addresses this challenge by using Kullback-Leibler divergence based hidden Markov models (KL-HMM). More precisely, the acoustic variability in the multi-accented speech is handled by using multilingual phoneme posterior probabilities, estimated by a multilayer perceptron trained on auxiliary data, as input feature for the KL-HMM system. With limited training data, we then build better acoustic models by exploiting the advantage that the KL-HMM system has fewer number of parameters. On HIWIRE corpus, the proposed approach yields a performance of 1.9% word error rate (WER) with 149 minutes of training data and a performance of 5.5% WER with 2 minutes of training data.