1. An apparatus for correcting errors in speech recognition, the apparatus comprising: a feature vector extracting unit extracting feature vectors from a received speech; a speech recognizing unit recognizing the received speech as a word sequence on the basis of the extracted feature vectors; a phoneme weighted finite state transducer (WFST)-based converting unit converting the recognized word sequence recognized by the speech recognizing unit into a phoneme WFST; and a speech recognition error correcting unit correcting errors in the converted phoneme WFST, wherein the speech recognition error correcting unit comprises a WFST synthesizing unit modeling a phoneme WFST transferred from the phoneme WFST-based converting unit as pronunciation variation on the basis of a Kullback-Leibler (KL) distance matrix, and wherein the KL distance is calculated by an equation 1, KL ( L - C i + R || L - C j + R ) = ∑ k = 1 M ω i , k KL ( b i , k || b j , k ) + ∑ k = 1 M ω i , k log ω i , k ω j , k. ( 1 )