In modern communication systems, the bandwidth of telephone speech is limited from 300Hz to 4 kHz, which reduces the intelligibility and naturalness of speech. Telephone speech bandwidth extension is researched to get wideband speech and to improve its intelligibility and naturalness, without increasing extra costs. This paper put forward an improved algorithm of speech bandwidth extension based on codebook mapping. In the process of codebook mapping, weighted coefficients were used to get mapping codebook. Objective tests show that spectral distortion of wideband speech obtained by this algorithm reduces at least 2%, comparing to conditional codebook mapping. Subjective tests show that the wideband speech obtained by this algorithm has better intelligibility and naturalness.