This paper proposes and investigates a coding and decoding scheme to achieve adaptive unequal error protection (UEP) using several convolutional codes which have different error-correcting capabilities. An appropriate encoder is selected to unequally protect each frame of information sequence according to the importance of the frame. Since the supplemental information of selected encoder is not sent for the sake of reducing redundancy, we assume that the decoder does not know which encoder was used, and the decoder has to estimate the used encoder. In order to estimate which encoder was used, the method using biased metric in Viterbi decoding is proposed. In decoding, however, there is a problem of Decoder-Selection-Error (DSE), which is an error that the decoder selected in a receiver does not correspond to the encoder used in a transmitter. An upper bound of DSE rate in decoding is derived. The proposed decoding scheme using the biased metric in a trellis can improve DSE rate and BER performance, because transition probability of encoders is taken into account in calculating likelihood by means of making branch or path metric biased. Computer simulation is employed to evaluate the BER performance and DSE rate of the proposed scheme. The performance is compared with a conventional equal error protection scheme and a UEP with the supplemental information on the used encoder. It is found that the proposed scheme can achieve better performance than them in case N=2.