We describe a kernel wrapper, a Mercer kernel for the task of phoneme sequence recognition which is based on operations with the Gaussian kernel, and suitable for any sequence kernel classifier. We start by presenting a kernel-based algorithm for phoneme sequence recognition, which aims at minimizing the Levenshtein distance (edit distance) between the predicted phoneme sequence and the true phoneme sequence. Motivated by the good results of frame-based phoneme classification using SVMs with Gaussian kernel, we devised a kernel for speech utterances and phoneme sequences, which generalizes the kernel function for phoneme frame-based classification and adds timing constraints in the form of transitions and durations constraints. The kernel function has three parts corresponding to phoneme acoustic model, phoneme duration model and phoneme transition model. We present initial encouraging experimental results with the TIMIT corpus.