Messages are generally selected with the same probability in the encoding scheme of rateless codes for equal error protection. In addition, a belief propagation (BP) decoding scheme is generally used because of the low computational complexity. However, the probability of recovering a new message by BP decoding is reduced if both the recovered and unrecovered messages are selected uniformly. Thus, more codeword symbols than expected are required for the perfect recovery of message symbols. Therefore, a new encoding scheme with a nonuniform selection of messages is proposed in this paper. In addition, a BP-Gaussian elimination hybrid decoding scheme that complements the drawback of the BP decoding scheme is proposed. The performances of the proposed schemes are analyzed and compared with those of the conventional schemes.