A quantization apparatus adapted to perform multiple-stage quantization of a parameter for a speech or image processing by using tree search, comprising: a search section adapted to match each of one or more of encoding targets with a code vector stored in a codebook to select a certain number of candidates including one in order of smaller quantization distortion; and a calculation section adapted to calculate a quantization error vector by subtracting the code vector from the target for each of the candidates, wherein in a first stage of the multiple-stage quantization, the search section is adapted to select a pre-specified number of candidates in order of candidates having smaller quantization distortion, characterized in that the quantization apparatus further comprises a candidate number determination section adapted to determine a number of candidates to be used in a subsequent stage by reducing by one from a number of candidates determined in a preceding stage, wherein in a second stage and in a stage subsequent to the second stage, the search section is adapted to select the number of candidates determined in the preceding stage, and in the case where the number of candidates determined in the preceding stage is not greater than a value P specified beforehand, the candidate number determination section is adapted to determine that, when a value of the quantization distortion is larger than a predetermined threshold value, the value P is used as the number of candidates in the subsequent stage, and to determine that, when the value of the quantization distortion is not greater than the predetermined threshold value, a value Q smaller than the value P specified beforehand is used as the number of candidates in the subsequent stage. a search section adapted to match each of one or more of encoding targets with a code vector stored in a codebook to select a certain number of candidates including one in order of smaller quantization distortion; and a calculation section adapted to calculate a quantization error vector by subtracting the code vector from the target for each of the candidates, wherein in a first stage of the multiple-stage quantization, the search section is adapted to select a pre-specified number of candidates in order of candidates having smaller quantization distortion, characterized in that the quantization apparatus further comprises a candidate number determination section adapted to determine a number of candidates to be used in a subsequent stage by reducing by one from a number of candidates determined in a preceding stage, wherein in a second stage and in a stage subsequent to the second stage, the search section is adapted to select the number of candidates determined in the preceding stage, and in the case where the number of candidates determined in the preceding stage is not greater than a value P specified beforehand, the candidate number determination section is adapted to determine that, when a value of the quantization distortion is larger than a predetermined threshold value, the value P is used as the number of candidates in the subsequent stage, and to determine that, when the value of the quantization distortion is not greater than the predetermined threshold value, a value Q smaller than the value P specified beforehand is used as the number of candidates in the subsequent stage.