1. An apparatus for recognizing continuous speech using search space restriction based on phoneme recognition, the apparatus comprising: a speech feature extraction unit for extracting a feature vector from an input speech signal; a phoneme recognition unit for recognizing phonemes based on the feature vector of the speech signal; and a phoneme-based speech recognition unit for recognizing a first word having corresponding first phoneme sequences from among the phonemes recognized by the phoneme recognition unit, and for constructing a connection word search network that includes connection words for the first word, wherein the phoneme-based speech recognition unit constructs the connection word search network to have a restricted search space based on the first word to perform a speech recognition process based on the connection word search network, wherein the phoneme-based speech recognition unit restricts connection words to be shifted at a boundary between words based on the first word to restrict a search space, and calculates a degree of similarity between the phoneme recognition result and the connection words to be shifted and shifts the phonemes to be recognized to a connection word having a degree of similarity equal to or higher than a predetermined reference value to restrict the search space, and wherein the phoneme-based speech recognition unit converts N phoneme sequences subsequent to the first phoneme sequences into a phoneme code, performs a logic AND operation on the phoneme code of the N phoneme sequences and the phoneme code of the connection word to be shifted, and does the sum of respective code values of the result of the AND operation to calculate the degree of similarity.