1. A feature-vector compensating apparatus for compensating a feature vector of a speech used in a speech processing under a background noise environment, comprising: a first storing unit that stores therein a compensation vector for compensating the feature vector of the speech for each of a plurality of noise environments; an feature extracting unit that extracts the feature vector of the speech in each of a plurality of frames of an input speech; an estimating unit that estimates a noise-environment series based on a feature-vector series that is a series of a plurality of extracted feature vectors for the frames and a degree of similarity that indicates a certainty that the feature vector is generated under the noise environment in each of a current frame and at least one of an immediately previous frame and an immediately subsequent frame of the current frame; a calculating unit that obtains a compensation vector corresponding to each noise environment in estimated noise-environment series based on the compensation vector present in the first storing unit; and a compensating unit that compensates the extracted feature vector of the speech based on obtained compensation vector.